cooperative formation control technology for manned ...... · lastly, the ﬂight control system is...

Cooperative Formation Control Technologyfor Manned/Unmanned Aerial Vehicles

Yu Zheng1(&), Teng Li2, Peixing Niu3, Mingxi Chen1, and Xu Zeng3

1 College of Automation Science and Electrical Engineering,BUAA, Beijing, China

{yzheng,chenmingxi}@buaa.edu.cn2 Aerospace, SATM, Cranfield University, Cranfield, England

[email protected] College of Aerospace Engineering, NUAA, YuDao Street 29, Nanjing, China

[email protected]

Abstract. This paper focuses on the cooperative formation of manned aerialvehicles (MAVs) and unmanned aerial vehicles (UAVs). Firstly, the charac-teristics of the MAV/UAVs and the mission assignment of MAV and UAVs inthe formation is analyzed, and the mathematical model of MAV and UAV arebuilt. At the same time, the relative kinematics equations of the MAV/UAVsformation based on Leader-Follower mode are also built. These work laysfoundation for the later research on cooperative operation of MAV/UAVs for-mation. Secondly, new formation shapes are designed referring the operationexperience of MAVs formation and considering the unique features ofMAV/UAVs formation. And these formation shapes are encapsulated into aformation library with which the fleet can expand or adjust the formationflexibly according to real battle demands. Moreover, UAV’s maneuvers aredesigned and these maneuvers are also encapsulated into a maneuver library.Lastly, the flight control system is designed for UAVs in order to enable them tofly stably following expected flight state. Furthermore, the management strate-gies of MAV/UAVs formation including formation organization, formationmaintain and formation reconstruction are analyzed based on the formationlibrary and maneuver library. The result of this paper is meaningful for boththeoretical research and practical application of MAV/UAVs formation.

Keywords: MAV/UAVs � Cooperative formation � Formation library �Maneuver library � Management strategies

1 Introduction

Multi-machine cooperative formation refers to a formation composed of multiplefighters. During the execution of the mission, each fighter cooperates with the targetdetection and attack, and the coordinated defense, complementing the tactics and air-borne weapons and equipments to improve operational efficiency and the success rateof completing a combat mission. In the traditional sense, multi-machine cooperativeformation generally refers to a formation formed by manned aerial vehicles (MAVs).With the development of Unmanned Aerial Vehicles (UAVs) technology, the concept

© Springer Nature Singapore Pte Ltd. 2019X. Zhang (Ed.): APISAT 2018, LNEE 459, pp. 2342–2367, 2019.https://doi.org/10.1007/978-981-13-3305-7_189

http://crossmark.crossref.org/dialog/?doi=10.1007/978-981-13-3305-7_189&domain=pdf



https://doi.org/10.1007/978-981-13-3305-7_189

of cooperative formation is expanded, and multi-machine collaboration can not onlyrefer to the coordination between multiple MAVs, but also the coordination betweenMAVs and UAVs, that is, the MAV/UAVs cooperative formation.

The MAV/UAVs cooperative formation usually consists of a MAV and multipleUAVs. The MAV is used as a leader commander to control multiple UAVs to performmissions [1]. In the formation cruise phase, the MAV and UAVs form a close formation.The MAV as the leader at the front of the formation can save fuel for the UAVs, increasethe cruising time, and also lead the UAVs formation to cross the narrow area to avoid thethreat. After arriving at the mission area, the MAV is located in a safe area outside theenemy’s firepower range to supervise the UAVs formation in real time. If necessary, theMAV can directly control the UAVs to perform the missions.

The MAV/UAVs cooperative formation is a complex combat system. In the back-ground of modern information warfare, the system includes not only fighter aircraft andUAVs platforms, but also the ground command centers, the satellites, the early warningaircraft and the battlefield communication system. It is a Space-Air-Ground integratedcombat system. In order to simplify the research process and highlight the researchfocus, this paper focuses on the collaborative control between MAV and UAVs.Therefore, firstly, the functions of the MAV and the UAVs in the cooperative formationare divided, so that the formation can not only exert the combat experience and decisionwisdom of the MAV pilots, but also exert the unique advantages of the UAVs [2].

In theoretical research, [3, 4] discuss several MAV/UAVs cooperative detectionand combat modes, and analyze the capability of MAV/UAVs cooperative formationplatform. The research team of National University of Defense Science and Technol-ogy has carried out research on MAV/UAVs cooperative mission control system andthe design and implementation of cooperative mission instruction [5, 6]. [7, 8] havethoroughly studied the effectiveness evaluation method of MAV/UAVs cooperativeformation combat. For MAV/UAVs cooperative target allocation, [9, 10] use discreteparticle swarm optimization (DPSO) to allocate targets for each UAV under centralizedarchitecture, considering the UAV’s air combat superiority index, target attack cost andbenefit [11, 12]. Emphasis is laid on the cooperative air combat decision-makingbetween MAVs and UAVs. The combat capability of UAVs formation is improved bythe decision-making superiority of manned aerial vehicles (MAVs).

The paper is organized as follows. Section 2 shows mathematical model andkinematics equations os MAV/UAVs. In Sect. 3, formation library and maneuverlibrary for MAV/UAVs formation are provided, whereas in Sect. 4, MAV/UAVsformation control based on maneuver library, is shown. Section 5, concludes the workand provides an overview of the MAV/UAVs cooperative formation control.

2 Mathematical Model and Kinematics Equations

Aircraft is a complex motion system. Strictly speaking, due to the continuous con-sumption of fuel during the actual flight, the mass and moment of inertia of the aircraftare time-varying, and the aircraft body will also have a certain deformation. In addition,the rotation of the Earth will cause centrifugal acceleration and Coriolis acceleration.With the change of flight altitude, the aerodynamic force of the aircraft and the flight

Cooperative Formation Control Technology for Manned/Unmanned Aerial Vehicles 2343

speed of the aircraft have a very complicated functional relationship. The mav/uavScooperative formation control problem is simplified by the following model of MAVand UAVs:

(1) Both the MAV and the UAVs are rigid bodies and do not undergo elasticdeformation;

(2) The quality, center of gravity and moment of inertia of MAV and UAVs areunchanged;

(3) Ignoring the influence of the curvature of the earth, regarding the surface of theearth as a plane, ignoring the influence of the rotation and revolution of the earth,and using the ground coordinate system as the inertial coordinate system;

(4) Since the altitude of the MAV/UAVs formation does not change much, it isassumed that the acceleration of gravity does not change with height and isconstant.

2.1 Dynamic Model of MAV/UAVs

In this paper, the nonlinear dynamic characteristics of MAV F18 and UAVs X47B arestudied, and a dynamic model of NAV and UAVs is established.

MAV F18 basic parameters UAVs X47B basic parameters

Wingspan 13.62 m Wingspan 18.92 mWing area 46.45 m2 Wing area 88.59 m2

Maximum takeoff weight 29938 kg Maximum takeoff weight 20215 kgThrust Each 65.3 kN Thrust 72 kNMaximum speed 1.8 Mach Maximum speed Subsonic speedCruising speed 0.9 Mach Cruising speed 0.9 MashLift limit 15000 m Lift limit 12190 m

2.1.1 Engine Thrust ModelThe MAV F18 has two engines and the UAV X47B has an one engine. It is assumedthat the engine thrusts of the two aircrafts are all along the ObXb axis of the machine,and the thrust components along the other two axes are zero. The models are:

TF18 ¼ 2dT fF18ðMa;HÞTX47B ¼ dT fX47BðMa;HÞ ð2:1Þ

Where T is the engine thrust, dT is the engine throttle opening degree, f ðMa;HÞ sthe maximum thrust that a single engine can output at the current Mach numberMa andflight altitude H.

2344 Y. Zheng et al.

2.1.2 Aerodynamic ModelThe aerodynamic forces of MAV and UAVs include lift, drag and lateral forces.

Llift ¼ 0:5qV2SwCL

D ¼ 0:5qV2SwCD

Y ¼ 0:5qV2SwCY

8><>: ð2:2Þ

Where CL, CD, CY are the lift coefficient, the drag coefficient and the lateral forcecoefficient, respectively, and

CL ¼ CL0 þCLaaþCLedeCD ¼ CD0 þCDt

CY ¼ CYbbþCYdrdr þCYppþCYr r

8><>: ð2:3Þ

It should be noted that for the lateral force coefficient, the X47B has no vertical tail,so the lateral force coefficient is only one side slip angle. And the air dynamic torquesof MAV/UAVs include pitching moment, rolling moment and yaw moment.

L ¼ 0:5qV2SwbCl

M ¼ 0:5qV2SwcACm

N ¼ 0:5qV2SwbCn

8><>: ð2:4Þ

Where the b is the span, cA is the mean geometric chord length of the wing, Cl, Cm,Cn are the rolling moment coefficient, the pitching moment coefficient, and the yawmoment coefficient, respectively. For the F18 fighter,

Cl ¼ ClbbþClada þCldr dr þClr r

Cm ¼ Cma¼0 þCmaaþCmdede

Cn ¼ CnbbþCndada þCn

drdr þCnppþCnr r

8><>: ð2:5Þ

For the X47B UAV, since there is no vertical tail, the term associated with thevertical tail in the aerodynamic derivative is zero, and

Cl ¼ ClbbþClada þCldr drCm ¼ Cma¼0 þCmaaþCmde

deCn ¼ Cn

dada þCn

drdr

8><>: ð2:6Þ

2.1.3 MAV/UAVs Motion EquationThe motion equations of MAV and UAVs are the same introduced here. The motionequations for MAV and UAV six-degree-of-freedom models need to be described bytwelve equations of state. The movement of a MAV or UAV includes linear motion


(the displacement of the center of mass, including front and back, left and right, up anddown) and angular motion (the rotation of the center of mass, including pitch, roll,yaw). Its differential equation can be expressed as:

f ð _x; x; uÞ ¼ 0y ¼ c � x

�ð2:7Þ

The 12 states of the MAV and the UAV x ¼ u v w / h w p q½r xg yg h �T are the components of the airspeed, the roll angle, the pitch angle, theyaw angle, the component of the angular motion along the axis of the body, the horizontalcoordinates and the flying height in the ground coordinate system. The input control in themodel u ¼ dT de da dr½ � is the engine throttle opening degree, the elevatordeflection angle, the aileron rudder deflection angle and the rudder deflection angle. It isimportant to note that the X47B UAV has no rudder, but the function of the rudder by theway of the cracked wing, which is used to express the same symbol for the convenience ofexpression.

Through formula deduction, The angular motion equation can be obtained:

_p ¼ ðc1rþ c2pÞqþ c3�Lþ c4N

_q ¼ c5pr � c6ðp2 � r2Þqþ c7M

_r ¼ ðc8pþ c2rÞqþ c4�Lþ c9N

8><>: ð2:8Þ

where c1 ¼ ðIy�IzÞIz�I2xzP , c2 ¼ ðIx�Iy þ IzÞIxzP , c3 ¼ IzP, c4 ¼ IxzP, c5 ¼ Iz�IxIy

, c5 ¼ Iz�IxIy

, c7 ¼ 1Iy,

c8 ¼ IxðIx�IyÞþ I2xzP , c9 ¼ IxP,P ¼ IxIz � I2xz.

The rotational motion equations of the center of mass can be obtained:

_/_h_w

24

35 ¼

1 sin/tanh cos/tanh0 cos/ �sin/

0 sin/cosh

cos/cosh

264

375 p

qr

24

35 ð2:9Þ

The linear motion equations of the center of mass can be obtained:

_X_Y_H

24

35 ¼

coshcosw sin/sinhcosw� cos/sinw sin/sinwþ coswsinhcos/coshsinw sin/sinhsinwþ cos/cosw �sin/coswþ sinwsinhcos/sinh �sin/cosh �cos/cosh

24

35 u

vw

24

35

ð2:10Þ

The force equations of the center of mass can be obtained:

m _V ¼ T � cosa � cosb� DþGxa � m � VmV _b ¼ �T � cosa � sinbþ Y � m � Vð�p � sinaþ r � cosaÞþGya � m � V � cosbmV _a ¼ �T � sina� LþmVð�p � cosa � sinbþ q � cosb� r � sina � sinbÞþGza

8<:

ð2:11Þ


2.2 Relative Kinematic Equation of a MAV/UAVs Formation

Defining the Leader-Follower formation control mode in the formation coordinatesystem. Assume that the coordinates of the follower F relative to the leader L are½x; y; z�, as shown in Fig. 1.

In the figure, the subscripts L and F indicate the leader and the follower, respec-tively; VL, VF , wL and wF are the speed and yaw angle of the leader and the follower,respectively; the definition wE is the yaw angle error of the leader relative to the follow,i.e. wE ¼ wF � wL.

According to the Coriolis equation, in the formation coordinate system, the relativespeeds of the leader and the follower are:

V fLF ¼ V f

F � V fL þx f

L � ðRfF � Rf

LÞ ð2:12Þ

In the formula, the superscript f represents the formation coordinate system; x fL is

the three components of the angular velocity along the coordinate axis of the longmachine in the formation coordinate system; Rf

L is the position of the leader in theformation coordinate system. Since the origin of the defined formation coordinatesystem is located in the centroid of the leader, its value is 0; 0; 0½ �; Rf

F is the position ofthe follower in the formation coordinate system x; y; z½ �. From this, the three-dimensional relative motion equation of the follower relative to the leader in theformation coordinate system can be obtained:

_x ¼ VF � coswE � coslE � _lL � zþ _wL � y� VL

_y ¼ VF � sinwE � coslE � _wL � x_h ¼ VF � sinlE � _l � xlE ¼ l f

F � l fL

wE ¼ w fF � w f

L

8>>>>>>><>>>>>>>:

ð2:13Þ

Fig. 1. Leader-follower formation relative position diagram


Where l fL l f

F are the track inclination angles of the leader and the follower in theformation coordinate system, respectively; lE is track inclination angle error of theleader relative to the follower.

3 Formation Library and Maneuver Library for MAV/UAVsFormation

3.1 Formation Library for MAV/UAV Formation

3.1.1 Design of MAV/UAV Formations ShapesThrough the analysis of the actual experience of MAV, it is known that fighters oftenform formations of different shapes according to different operational environments andmission requirements: parallel formations are mainly used to expand the search rangewhen searching for targets; vertical formations are mainly used for bombing, airdrops,airborne and avoiding threat or pass narrow areas; trapezoidal teams are often used forcoordinated ground attack; wedge formations teams are often used for cruising andbombing; snake formations are often used for large formations; diamond formations aremainly used to protect important targets in formations, such as early warning aircraft;reverse arc formations are often used for interception of enemy aircraft; and arrowformations are mainly used for penetration, air attack on enemy important targets andnuclear strike against the enemy.

As shown in Fig. 2, in order to facilitate the formation of formation, this paper isused dx dy dz½ �T to represent the relative position of two UAVs or between theMAV and the UAVs, which dx represents the longitudinal distance, dy representing thelateral distance, and dz indicates the height difference. In this paper, a combinationformation of a F18 and four X47B UAVs is used as an example to design 5 formation.When the number of UAVs increased, it can be expanded according to the formationcharacteristics.

1. Parallel formation

In the parallel formation, the UAVs are arranged at the same height in parallel, sodx ¼ dz ¼ 0, according to the search capabilities of UAV’s detection equipments toadjust dy (Fig. 3).

Fig. 2. Distance between two UAVs


2. Vertical formation

In the vertical formation, the UAVs are arranged at the same height in vertical, sody ¼ dz ¼ 0, according to the required safety distance at the current flight speed toadjust dx (Fig. 4).

3. Trapezoidal formation

In the trapezoidal formation, the UAVs are arranged at the same height in vertical,dz ¼ 0, according to the specific combat missions to adjust the parallel distance dx andvertical distance dy (Fig. 5).





4. Wedge formations

In the triangle formation, the UAVs are distributed at the same height in triangular,when the relative distance of follower UAVs and leader UAV is:

d ¼ dx dy dz½ �T¼ 2b ðbpÞ=4 0½ �T ð3:1Þ

the follower UAVs can obtain the optimal aerodynamic efficiency, where b is thelength of Wing (Fig. 6).

5. Diamond formation

In the prismatic formation, the UAVs are distributed at the same height in pris-matic, so dz = 0, and according to the required safety distance at the current flightspeed to adjust dx and dy (Fig. 7).

3.1.2 Building of MAV/UAV Formations LibraryIn order to reduce the workload of the MAV pilots, this paper builds a formationlibrary for the MAV/UAVs. The formation of the common formation parameters arestored in the formation library, the MAV pilots can set the corresponding formationdata for each UAV as long as the number of UAVs and the required formation are set,and the UAVs automatically form formation according to the information received bythe MAV.




As shown in Fig. 8, the MAV pilot sends information on the formation commandto the formation library, including the type of formation Type, the number of UAVsNumber, and the distance information dx; xy; xz of the UAV in the formation, thenposition distribution information of each UAV in the formation coordinate system canbe generated, and the information is wirelessly transmitted to each UAV. The autopilotof UAV is controlled to maintain UAV formation flying according to the receivedformation information.

3.2 Design of Maneuver Library and Maneuver Action Selection Module

The path of UAV can be composed of a series of maneuvers. In this paper, UAV routecontrol is realized based on basic operation maneuver. As shown in Fig. 9, the principleis that the maneuver selection module determines what kind of maneuver the UAVshould take according to the preset route point information and the current position ofthe UAV. According to the required maneuver information, the correspondingmaneuver model is selected in the basic operation maneuver library, and the UAV’sroute is automatically generated by the maneuver model. Then the UAV autopilotcontrols the UAV to automatically fly along the route according to the generated routeinformation.

3.2.1 Design of MAV/UAV Maneuver LibraryCommonly used fighter maneuver libraries can be divided into basic operationalmaneuvering libraries and typical tactical maneuvering libraries. The basic operationmaneuver library was proposed by NASA scholars and includes the following sevenbasic maneuvers: ① constant control amount; ② maximum acceleration; ③ the

Fig. 8. Formation library structure

Fig. 9. Principle of UAV route flight based on maneuver library


maximum deceleration; ④ maximum overload pull up; ⑤ maximum overload sub-duction; ⑥ maximum overload left turn; ⑦ Maximum overload turns right.A schematic diagram of the seven basic operational maneuvers is shown in Fig. 10.

The above seven basic operational maneuvers are based on maximum overload, butfor formation control, the UAV does not need to always do the maximum overloadwhen doing maneuvers. Therefore, this paper makes appropriate modifications on thebasis of the above seven basic operational maneuvers, making it more suitable for theformation of formation control. The modified seven basic operational maneuvers are:① constant control amount; ② uniform acceleration; ③ uniform deceleration; ④ pullup; ⑤ subduction; ⑥ fixed overload left turn; ⑦ fixed overload right turn.

According to the characteristics of the above seven basic operational maneuvers,they can be divided into three types: linear maneuver, turning maneuver, pull up andsubduction maneuver, as shown in Fig. 11. Flight maneuvers in other three-dimensional spaces can be combined by the above three types of maneuvers.

Fig. 10. Seven basic operational maneuvers

Fig. 11. Basic operational maneuver classification


1. Linear maneuver

Linear motion is the most basic and most commonly used maneuver, includingconstant control, uniform acceleration, and uniform deceleration. Assume that thestarting point of the straight flight segment is SðXs; Ys;Hs;ws; vsÞ, and the end point isEðXe; Ye;He;we; veÞ. The straight line distance between two points is:

Lse ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðXe � XsÞ2 þðYe � YsÞ2 þðHe � HsÞ2

qð3:2Þ

Then the tangential overload of the drone is:

nx ¼ v2e � v2s2g � Lse ð3:3Þ

2. Turning maneuver

Turning maneuvers include fixed overload left turn and fixed overload right turn.During turning, the side slip angle of the UAV will increase the air resistance of theaircraft, which is not conducive to maneuvering. Therefore, this paper designs theturning maneuver of the UAV based on coordinated turning. When the UAV is doing acoordinated turning flight, the vertical component of the lift is counteracted by thegravity of the UAV, and the lift component in the horizontal direction provides thecentripetal force required for the UAV to provide a turn.

mg ¼ L cos/

mV2

R¼ L sin/

8<: ð3:4Þ

The roll angle and turning radius of UAV during coordinated turn are:

/ ¼ arctan nz ð3:5Þ

R ¼ v2

nz � g ð3:6Þ

3. Pull up and subduction maneuver

Pull up and subduction maneuvers are similar to turning maneuvers. They are alsoachieved by uniform circular motion. The lift of the UAV subtracts the component ofgravity along the radial direction to provide centripetal force.

L� mg cosðh� aÞ ¼ mv2

Rð3:7Þ


At this time, the normal overload of the UAV and the subduction maneuver is:

nz ¼_hvg

ð3:8Þ

The maneuvering radius of the pull up or subduction maneuver is:

R ¼ v2

nz � g ð3:9Þ

The basic operational maneuver library consisting of seven basic operationalmaneuvers is shown in Table 1:

A typical tactical maneuver library contains a variety of typical tactical maneuvers,while a typical tactical maneuver can be composed of basic operational maneuvers.This paper demonstrates the generation of typical tactical maneuvers from basicoperational maneuvers through jump maneuver, serpentine maneuver, and 8-characterpatrol maneuvers.

1. Jump maneuver

As shown in Fig. 12, the jump maneuver can be composed of the basic operationalmaneuver that pulls up during the jump, the basic control maneuver that graduallyincreases the height during the jump, and the basic operational maneuver that changesthe dive when the jump is raised.

Table 1. Basic operation maneuver library commands

Maneuver command Basic operation maneuver1 2 3 4 5 6 7

nx 0 n1 �n1 0 0 0 0nz 0 0 0 �n2 n2 �n2 n2c 0 0 0 0 0 �c1 c1

0 2 46

-20

240

1

2

3

4

5

6

X/kmY/km

H/k

m

Fig. 12. Schematic and simulation diagram of jumping maneuver


2. Serpentine maneuver

As shown in Fig. 13, the serpentine maneuver can be composed of constant controlmaneuvers, fixed overload left turn maneuvers, and fixed overload right turn maneuversin the basic operational maneuver library.

3. 8-character patrol maneuvers

As shown in Fig. 14, similar to the Serpentine maneuver, the 8-character patrolmaneuver is also composed of constant control maneuvers, fixed overload left turnmaneuvers and fixed overload right turn maneuvers. In this maneuvering action, themaneuvering route connections of the various sections of the UAV form an “8” shape.

3.2.2 Design of Maneuver Action Selection ModuleThe maneuver selection module of the UAV calculates variation of the track inclinationangle and the change of the azimuth of the track between the two adjacent track pointsaccording to the desired track point information, and then determines which maneuveraction of the UAV to carry out according to these information. The selection process ofmaneuver is shown in Fig. 15, where Dl is the change of the track inclination angle of

05

1015

2025

05100

2

4

6

8

10

H/k

m

Y/kmX/km

Fig. 13. Schematic and simulation diagram of serpentine maneuver

05

1015

05

102

4

6

8

H/k

m

Y/km X/km

Fig. 14. Schematic and simulation diagram and of 8-character patrol maneuvers


the adjacent two track points, and Du is the change of the track azimuth angle of theadjacent two track points.

It can be seen from the maneuver selection process that when the track inclinationangle change amount and the track azimuth angle change amount of the adjacent twotrack points are not zero, the UAV performs a three-dimensional space combinedmaneuver, and the maneuver is composed of pull up or subduction maneuver and turnmaneuver.

4 MAV/UAVs Formation Control Based on ManeuverLibrary

4.1 Formation Organization of MAV/UAVs Formation

When MAV/UAVs formation performs a mission, MAV and UAVs need to take off atregular intervals from the airport or aircraft carrier flight deck. Generally, the MAVtakes off first. After the takeoff, the MAV pilot sends a takeoff command to each UAVto confirm that the UAV takes off in sequence. When all the UAVs took off, the MAVand the UAVs were arranged at a distance from each other. Before arriving at themission area, the formations usually fly in tight wedges to save fuel. This paperintroduces two ways to construct a wedge formation: straight-line catch-up collection,180° turn collection.

1. Straight-line catch-up collection

In this collection mode, the leader flies in a straight line at a slower flight speedafter takeoff, and the UAVs that takes off later speeds up to catch up with the longplane. When the relative position to the desired position of the leader is reached, thesame speed as that of the leader is followed to fly in a straight line until all the UAVsreach the predetermined relative position with the leader (Fig. 16).

Fig. 15. Maneuver action selection process


2. 180° turn collection

In this collection mode, all aircraft fly at a faster speed after takeoff, and thedistance between the aircraft is reduced by a 180° turn. The MAV turns first, and thesubsequent UAVs turn in a closer distance from the airport, so that the distance of theaircraft can be quickly reduced by reducing the flight distance of the subsequent UAVs.Then the formation is transformed into a wedge formation, which is piloted by MAV(Fig. 17).

4.2 Formation Maintain of MAV/UAVs Formation

The formation maintenance is in the formation coordinate system, and each UAVmaintains a relative position with the MAV. The formation maintain is very importantfor MAV/UAVs formation flight, especially in tight formations, if accurate formation isnot maintained, the formation will not obtain the best aerodynamic effects and mayhave a collision.

The formation maintenance strategy adopted in this paper: the leader MAVtransmits its flight state (including position, altitude, speed, heading angle, etc.) to eachUAV in real time, and each UAV maintains its relative position with the leader MAVby adjusting its own speed, altitude, heading, etc.

Fig. 16. Schematic diagram of Straight-line catch-up collection

Fig. 17. Schematic diagram of 180° turn collection


The control structure of formation maintain is shown in Fig. 18. In the figure, ex, ey,eh is the relative position error between the UAV and the leader MAV in the formationcoordinate system, respectively.

ex ¼ dtx � dxey ¼ dty � dy

eh ¼ dth � dh

8><>: ð4:1Þ

Where dtx, dty, d

th is the relative position of the UAV and the leader MAV in the

formation coordinate system at time t; dx, dy, dh is the expected relative distance of acertain formation in the formation coordinate system.

dtxdtydth

264

375 ¼

coswL sinwL 0� sinwL coswL 0

0 0 1

24

35 X � XL

Y � YLH � HL

264

375 ð4:2Þ

_ex_ey_eh

264

375 ¼

coswL sinwL 0� sinwL coswL 0

0 0 1

24

35 Vx � VL

xVy � VL

y

Vh � VLh

24

35 ð4:3Þ

The output of the formation maintain controller is:

Vc ¼ Vt þ kvpex þ kvi

Z t

0exdtþ kvd _ex

wc ¼ wt þ kwp ey þ kwi

Z t

0eydtþ kwd _ey

Hc ¼ Ht þ khpeh þ khi

Z t

0ehdtþ khd _eh

8>>>>>>><>>>>>>>:

ð4:4Þ

Where Vt, wt, Ht is the current flight speed, heading angle and altitude of the UAV.

Fig. 18. Formation maintain control structure


4.3 Formation Reconstruction of MAV/UAVs Formation

The problem of formation reconfiguration is to find a scheme that meets low fuelconsumption and formation adjustment quickly, which makes the formation of aMAV/UAVs formation from one formation to another formation in the case of nocollision between the MAV and UAVs. Before the formation reconstruction, theposition of the new formation must be assigned to each UAV. The route required forthe UAV from the current position to the position in the new formation should be avoidcrossover.

4.3.1 Formation Reconstruction StrategyThis paper introduces the process of formation reconstruction based on the execution ofthe ground attack mission by the MAV/UAVs formation. Before the formationreconstruction, the MAV pilot can input the corresponding formation type and distanceparameters to the formation library to obtain the desired position of each UAV in thenew formation.

1. The transformation between wedge close formation and vertical formation

This formation transformation is mainly used in the course of sailing and returning.When the formation need to pass through narrow airspace to avoid obstacles or groundradar threats, they need to be transformed from wedge close formation into longitudinalformation. Then the formation need to be re-converted into wedge close formationsafter passing through narrow airspace. In the process of formation reconstructioninvolving the wedge close formation, in order to avoid collision between the UAV orthe MAV, it is necessary to make a transition through a relatively wedge loose for-mation with a large distance. When the formation is changed, the outermost UAVdecelerates first, and the inner UAV is decelerates after reaching a safe distance. asshown in Fig. 19.

In the close formation, the lateral distance between the leader MAV and the fol-lower UAVs is dy ¼ pb=4, the vertical distance dz ¼ 0, and the longitudinal distancedx ¼ 2b can obtain the best aerodynamic effect, which b is the length of the leaderMAV.

Fig. 19. Schematic diagram of the transformation process from wedge formation to verticalformation


2. The transformation between wedge close formation and trapezoidal formation

After the MAV/UAVs formation arrives at the mission area, the MAV is removedfrom formation to the safe area, and the formation of the UAV formation is transformedinto a trapezoidal formation to perform the attack mission. Similar to the former for-mation transformation, this formation transformation must first be transformed into arelatively wedge loose formation. Then the MAV moves away from the UAV for-mation through the jump maneuver. The UAV is formed into a trapezoidal formationby maneuvering such as uniform acceleration, uniform deceleration, fixed overload leftturn, and fixed overload right turn, as shown in Fig. 20. Generally, when the MAVremoves the formation, UAV1 is used as the leader of the UAV formation, and otherUAVs perform the formation transformation by adjusting the relative position of theleader UAV.

3. The transformation between attacking wedge formation and trapezoidal formation

When multiple UAVs form a trapezoidal formation to attack a ground targets, thefirst UAV will evaluate the attack after attacking the target. If the target is not com-pletely destroyed, a second attack is required. At this time, if the UAV is transferred tothe target to re-attack the target, no one has the opportunity to waste precious time andfuel around the road due to the turning radius problem. At this point, the rear UAV willsolve the problem of secondary attack.

In addition, the UAV ammunition that has already executed the attack mission isnot enough to return to the rear of the formation. The ammunition-rich UAVs attackedthe new target and changed from the trapezoidal formation to the wedge formation.And the UAVs carry out a round attack on the new target in turn (Fig. 21).

Fig. 20. Schematic diagram of the transformation process from wedge close formation andtrapezoidal formation


4.3.2 Formation Reconstruction Speed Command CalculationIn the process of formation reconfiguration, the initial speed and the termination speedof each UAV are the same as that of the leader, but the length of the route experiencedby each UAV is different, so uniform acceleration and uniform deceleration maneuverare needed to eliminate the formation. The distance of each UAV during the recon-struction process.

As shown in Fig. 22, the formation reconstruction starts at time T1 and ends at timeT2. When the length of the route of a UAV is greater than that of the leader, the UAVundergoes① uniform acceleration; ② constant control amount;③ uniform decelerate.DVmax and DVmin are the maximum and minimum changes in the relative leader flightspeed T, respectively.

DVmax ¼ Vmax � V

DVmin ¼ Vmin � V

(ð4:5Þ

Where Vmax Vmin is the maximum speed and minimum speed that the UAV canstabilize flight.

Fig. 21. Schematic diagram of trapezoidal formation and wedge formation

Fig. 22. Speed change curve of UAV in formation reconfiguration process


The route difference between the UAV and the leader is:

DL ¼Z T2

T1

DVðtÞdt ð4:6Þ

In order to complete the formation reconstruction as quickly as possible, the UAVperforms uniform acceleration and uniform deceleration maneuvers with the maximumlongitudinal acceleration that can be achieved. Assuming that the acceleration in theuniform acceleration phase is a1, and the acceleration in the uniform deceleration phaseis a2, the speed command of the UAV formation reconstruction process is:

Vc ¼V þ a1ðt � T1Þ t 2 ½T1; T3�Vmax t 2 ðT3; T4ÞVmax � a2ðt � T4Þ t 2 ½T4; T2�

8<: ð4:7Þ

When the UAV’s route difference is DL�V2maxða1 þ a2Þ=ð2a1a2Þ, the UAV will do

the uniform acceleration maneuvering and then do the uniform deceleration maneuverwithout going through the intermediate uniform speed process. When the length of theUAV’s route is less than the leader, the UAV will do the acceleration maneuveringafter the deceleration maneuver.

4.4 Simulation Verification of Formation Control of MAV/UAVsFormation

4.4.1 Simulation Verification of Formation OrganizationTaking the Straight-line catch-up collection as an example to verify the formationorganization process. The MAV took off first, then flew in a straight line at a speed of160 m/s. After the UAV took off, it chased the MAV at a speed of 260 m/s. At theinitial time of simulation, the speed direction of the MAV and each UAVs is along thehorizontal of the X axis, the heading angle w ¼ 0� and the roll angle / ¼ 0�. The initialposition and the expected relative position to the leader are shown in Table 2 (Fig. 23).

Table 2. MAV and UAVs initial position and expected relative position information (one)

Number Initial position (X, Y, H) Expected relative position to the leader (dx, dy, dz)

L (40000, 0, 8000) ——

F1 (30000, 0, 8000) (−100, 0, 0)F2 (20000, 0, 8000) (−200, 0, 0)F3 (10000, 0, 8000) (−300, 0, 0)F4 (0, 0, 8000) (−400, 0, 0)


4.4.2 Simulation Verification of Formation MaintainTaking the leader uniform turning and climbing as an example to verify the formationmaintain process.

The initial speed of the MAV L and the UAV F1-F4 is 260 m/s, the speed directionis the horizontal direction along the X axis, the heading angle w ¼ 0�, the roll angle/ ¼ 0�, and the leader makes a uniform turning and climbing flight. The initial positionof the MAV and the UAVs and the relative position of the UAV and the leader in theformation are shown in Table 3. At the initial moment, there is no relative positionerror between the four UAVs and the leader.

(a) (b)

(c) (d)

0 200 400 600150

200

250

300

t/s

V/(m

/s)

F1F2F3F4L

446 446.2 446.4 446.6 446.8

159.96

159.98

160

160.02

160.04

160.06

t/s

V/(m

/s)

F1F2F3F4L

0 200 400 600-4

-3

-2

-1

0x 10

4

t/s

dx/m

F1F2F3F4

100 200 300 400 500-1200

-1000

-800

-600

-400

-200

0

t/s

dx/m

F1F2F3F4

Fig. 23. Simulation curve of Straight-line catch-up collection. (a) is flight speed, (b) is UAV F4 flightspeed partial enlarged drawing, (c) is longitudinal relative distance between each UAV and MAV.

Table 3. MAV and UAVs initial position and expected relative position information (two)


L (0, 0, 8000) ——

F1 (−500, −500, 8000) (−500, −500, 0)F2 (−500, 500, 8000) (−500, 500, 0)F3 (−1000, −1000, 8000) (−1000, −1000, 0)F4 (−1000, 1000, 8000) (−1000, 1000, 0)


As shown in Fig. 24(d), the flight speed of the MAV and each UAV is 260 m/s atthe initial time. When the stable formation flight state is reached, the speed of the UAVon the inner side of the arc slows down, and the more the inside speed is reduced.Similarly, the speed of the UAV located outside the arc increases accordingly. It can be

(a) (b)

(c) (d)

(e) (f)

0 500010000

-20000

2000790079508000

805081008150

X/mY/m

H/m

0 5000 10000-3000

-2000

-1000

0

1000

2000

3000

4000

X/m

Y/m

0 10 20 30 407980

8000

8020

8040

8060

8080

8100

t/s

H/m

F1F2F3F4L

0 10 20 30 40254

256

258

260

262

264

266

t/s

V/(m

/s)

F1F2F3F4L

0 10 20 30 40-2

0

2

4

6

8

t/s

ψ/d

eg

F1F2F3F4L

0 10 20 30 40-3

-2

-1

0

1

2

3

t/s

ex/m

F1F2F3F4

Fig. 24. Simulation curve of the leader uniform turning and climbing. (a) is three-dimensionaltrack, (b) is X-Y plane track, (c) is flight height, (d) is flight speed, (e) is yaw angle, (f) is positionerror in the X-axis direction in the formation coordinate system, respectively.


seen from Fig. 24(f)-(h) that the longitudinal position error of each UAV converges tozero at 18 s, the lateral position error converges to zero at 30 s, and four UAVs exist inthe height direction −0.45 m position error.

4.4.3 Simulation Verification of Formation ReconstructionTaking a tight wedge formation into a vertical formation as an example to verify theformation reconstruction process. The initial speed of the MAV L and the UAV F1-F4is 260 m/s, the speed direction is the horizontal direction along the X axis, the heading

Table 4. MAV and UAVs initial position and expected relative position information (three)


L (0, 0, 8000) ——

F1 (−27, −10.7, 8000) (−50, 0, 0)F2 (−27, 10.7, 8000) (−100, 0, 0)F3 (−54, −21.4, 8000) (−150, 0, 0)F4 (−54, 21.4, 8000) (−200, 0, 0)

(a) (b)

(c) (d)

0 10 20 30 40240

245

250

255

260

265

t/s

V/(m

/s) F1

F2F3F4L

0 10 20 30 40-3

-2

-1

0

1

2

3

t/s

ψ/d

eg

F1F2F3F4L

0 10 20 30 40-250

-200

-150

-100

-50

0

t/s

dx/m

F1F2F3F4

0 10 20 30 40-30

-20

-10

0

10

20

30

t/s

dy/m

F1F2F3F4

Fig. 25. Simulation curve of from close wedge formation to a vertical formation. (a) is flightspeed, (b) is yaw angle, (c) is longitudinal distance between each UAV and MAV, (d) is lateraldistance between each UAV and MAV.


angle w ¼ 0�, the roll angle / ¼ 0�, and the leader makes a Uniform straight flight.The maximum acceleration of the UAV when making a uniform deceleration maneuveris 2m

�s2, the maximum acceleration of the uniform acceleration maneuver is 1:5m

�s2.

The initial position of the MAV and the UAVs and the relative position of the UAVand the leader in the formation are shown in Table 4.

It can be seen from Fig. 25 that when the MAV/UAVs formation is changed from aclose wedge formation to a vertical formation, the four UAVs first make a uniformdeceleration maneuver and then make a uniform acceleration maneuver to increase thefront-back distance between each other. In order to ensure safety, the UAV3 and UAV4located outside the formation will be uniformly decelerated at 5 s, and the UAV1 andUAV2 on the inside of the formation will be evenly decelerated after 10 s. When allUAVs reach a safe front-to-back distance, they begin to adjust the lateral position in theformation and keep flying in the same straight line as the MAV. The entire formationtransformation process takes about 23 s.

5 Conclusion

In this work, we presented the relative kinematics equations of the MAV/UAVs for-mation based on leader-follower mode. We designed formation library and maneuverlibrary for MAV/UAVs formation and considering the unique features of MAV/UAVsformation. And these formation shapes are encapsulated into a formation library withwhich the fleet can expand or adjust the formation flexibly according to real battledemands. Moreover, UAV’s maneuvers are designed and these maneuvers are alsoencapsulated into a maneuver library. Lastly, the flight control system is designed forUAVs in order to enable them to fly stably following expected flight state. Further-more, the management strategies of MAV/UAVs formation including formationorganization, formation maintain and formation reconstruction are analyzed based onthe formation library and maneuver library. The simulation results show that theexpected requirements can be achieved. The result of this paper is meaningful for boththeoretical research and practical application of MAV/UAVs formation.

References

1. Gao C, Zhen Z, Gong H (2016) A self-organized search and attack algorithm for multipleunmanned aerial vehicles. Aerosp Sci Technol 54:229–240

2. Shukla A, Karki H (2015) Application of robotics in onshore oil and gas industry-a reviewPart I. Robot Auton Syst 75(PB):490–507

3. Xiaowen S (2014) Mode and capability requirement analysis of manned/UAV cooperativeair combat. J Chin Acad Electron Sci 9(4):331–334

4. Zhaowang F, Yingxin K et al (2012) Analysis of cooperative air combat mode and capabilityrequirement for manned/unmanned combat air vehicles. Fire Control Command Control 37(1):73–77

5. Hui P, Xiaojia X et al (2008) MAV/UAVs collaborative mission control system. J Aviat29:135–141


6. Lizhen W, Yuan L et al (2008) Design and implementation of cooperative mission commandset for MAV/UAVs. J Syst Simul 20:517–521

7. Xiaohui Y (2013) Research on MAV/UAVs collaborative operational effectivenessevaluation

8. Yanfei D, Wang Z et al (2013) Comprehensive index model for MAV/UAVs collaborativeair-ground attack effectiveness evaluation

9. Wanjun L et al (2012) MAV/UAVs group cooperative air combat target allocation algorithm10. Yusong F et al (2011) Multi target assignment for MAV controlled UAV air combat11. Jun C et al (2015) MAV/UAVs mixed formation limited intervention collaborative decision

making. J Aviat 36(11):3652–366512. Xun W et al (2015) Decision making for coordinated operation of MAVUAVs formation.

Comput Simul 32(9):128–13213. Kumar M, Cohen K, Homchaudhuri B (2012) Cooperative control of multiple uninhabited

aerial vehicles for monitoring and fighting wildfires. J Aerosp Comput Inf Commun 8(8):1–16


cooperative formation control technology for manned ...... · lastly, the ﬂight control system is...

Documents