Analysis on Hover Control Performance of T- and Cross ...

Research ArticleAnalysis on Hover Control Performance of T- and Cross-ShapedTail Fin of X-Wing Single-Bar Biplane Flapping Wing

Pingxia Zhang 1 Junru Zhu2 and Yongqiang Zhu 1

1School of Mechanical and Automotive Engineering Qingdao University of Technology Qingdao 266520 China2Pegasus California School Qingdao 266105 China

Correspondence should be addressed to Yongqiang Zhu yongqiangzhu163com

Received 3 April 2020 Revised 22 May 2020 Accepted 2 June 2020 Published 21 July 2020

Academic Editor Weitian Wang

Copyright copy 2020 Pingxia Zhang et al+is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e current flapping wing adopts T-shaped or cross-shaped tail fin to adjust its flight posture However how the tail fin will affectthe hover control is not very clear So the effects of the two types of tail on flight will be analyzed and compared by actual flighttests in this paper Firstly we proposed a new X-wing single-bar biplane flapping-wing mechanism with two pairs of wings+ereafter the overall structure gearbox structure tail frame and control system of the flapping wing were designed andanalyzed Secondly the control mechanism of hover is analyzed to describe the effect of two-tail fin on posture control+irdly theBeetle was used as the control unit to achieve a controllable flight of flapping wing+eMPU6050 electronic gyroscope was used tomonitor the dronersquos posture in real time and the Bluetooth BLE40 wireless communication module was used to receive remotecontrol instructions At last to verify the flight effect two actual flapping wings were fabricated and flight experiments wereconducted +e experiments show that the cross-shaped tail fin has a better controllable performance than the T-shaped tail fin+e flapping wing has a high lift-to-mass ratio and good maneuverability +e designed control system can achieve the con-trollable flight of the flapping wing

1 Introduction

Flying creatures of nature all use a flapping wing to fly +eyflap wings and change the angle and shape of their wing andtail fin to create lift and propulsion and change the di-rection of flight and flight mode By doing these they caneasily realize the rapid and flexible flight movements [1]such as flying gliding and hovering +en they can havevery high mobility and flexibility of the flight and realize ahigh structural pattern of a pair of wings with multiplefunctions Especially hummingbirds have good hoveringflight performance as shown in Figure 1 +is inspired us todesign a small smart and flexible drone

An ornithopter is a drone whose wings flutter up anddown like birds or insects Most researches contributeand innovate in the following aspects wing shapeanalysis [2 3] the aerodynamics of flapping wing [4ndash7]power extraction performance of semiactive flappingairfoils [8] mechanism [9ndash11] different actuation

mechanisms hybrid actuation mechanisms [12] elec-trical motor-driven method mechanical transmission-driven method and ldquoartificial musclerdquo material-drivenmethod [13]

At present the flapping-wing drone that can successfullyfly can be divided into forward flight and hover flight fromthe flight function and can be divided into two categoriesfrom the presence or absence of the tail the tailless (Figure 2)and the tailed+e tailed flapping-wing drone can be dividedinto three types horizontal tail fin (Figures 3(e) 3(g) 3(h)and 3(k)) T-shaped tail fin (Figures 3(a) 3(b) 3(f) 3(i) 3(j)and 3(l)) and cross-shaped tail fin (Figures 3(c) and 3(d))+ese research studies provide great contribution and in-novation for making flapping wing to successfully fly If thetail structure is too complicated it will increase the weight ofthe tail and make the drone difficult to fly So the tail of theactual flapping-wing drone will not be too complicated andfor easy control most of the flapping-wing drones use T-and cross-shaped tail fin

HindawiJournal of RoboticsVolume 2020 Article ID 8880338 13 pageshttpsdoiorg10115520208880338

Figure 1 Hummingbirds can hover easily by changing the angle and shape of their wings and tail fin

(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k) (l)

Figure 2 Motor-driven insect-inspired tailless FWMAVs capable of free controlled flying (a) Nano Hummingbird developed by Aer-oVironment Inc [14] (b) TechJect Dragonfly developed by TechJect Inc [15] (c) BionicOpter developed by Festo AG amp Co KG [16] (d)eMotionButterflies developed by Festo AG amp Co KG [17] (e) Robotic Hummingbird developed by Texas AampM University [18] (f )KUBeetle developed by Konkuk University [19] (g) Colibri robot developed by the Universite Libre de Bruxelles [20] (h) RoboticHummingbird developed by Purdue University [21] (i) Quad-thopter developed by Delft University of Technology [22] (j) NUS-Robobirddeveloped by the National University of Singapore [23] (k) DelFly Nimble developed by the Delft University of Technology [24] (l)Butterfly-type ornithopter developed by Beihang University [25]

(a) (b) (c) (d)

(e) (f ) (g) (h)

(i) (j) (k) (l)

Figure 3 Examples of existing bird-inspired tailed FWAVs (a) Microbat from AeroVironment Inc [26] (b) 32 g ornithopter from KonkukUniversity [27] (c) DelFly Explorer from the Delft University of Technology [28] (d) SmartBird from Festo AG amp Co KG [29] (e) RoboRaven V from the University of Maryland [30] (f ) H2Bird ornithopter from the University of California Berkeley [31] (g) Robird fromClear Flight Solutions and the University of Twente [32] (h) BionicBird from httpbionicbirdcom (i) 32 g flapping-wing platform fromHarvard University [33] (j) NAV from the American University of Sharjah [34] (k) Slow Hawk 2 from Kinkade RC (l) Butterflyrsquos spydrone from Israel Aircraft Industries (IAI) [35]

2 Journal of Robotics

For ornithopter it is more difficult to hover like ahummingbird since its aerodynamic [36 37] and mecha-nism [38] are more complex Moreover it should producemore drag force to balance gravity and be controlled betterthan flying forwards only [39ndash42] And the hovering flap-ping wing has more flying potential +erefore many re-searchers carry out stability analysis of near-hovering [43] orhovering [44 45] and use various control strategies such asadaptive control [46] passive stability enhancement [47]Spiking Neural Network (SNN) control [48] sliding-modeapproach [49 50] and adaptive feedforward schemes [51]However these make the ornithopter adopt more powerfulcontrol unit and more expensive

Moreover at present the ornithopter adopts mostly thestructure of imitating birdsrsquo wings [52]mdashthe whole orni-thopter only has one pair of wings Due to the great dif-ference in the freedom and flexibility between theornithopter and birdsrsquo wings the lift of the ornithopter willdecrease when the wings are flapped upwards +ereforespecial structures need to be designed to compensateresulting in complex wing structures [53ndash55] and increasedweight of the ornithopter

In addition few papers have analyzed the influence ofthe tail fin shape on the hovering effect

+erefore in this paper we designed a new X-wingsingle-bar biplane flapping-wing flight vehicle to imitate thehummingbird vertical hovering flight +en we analyzedand compared hover performance of two kinds of tail fin

+e remaining sections of this article are organized asfollows in the second section the structure of the X-wingflapping-wing drone is designed It can further enhanceflight thrust through the synchronization of two pairs ofwings beat-up and squeeze the air vortex flow +erefore itcan both generate thrust while flapping up and down In thethird section the control mechanism of the T-shaped andcross-shaped tail fin is analyzed +en the control variablesand implementation are proposed In the fourth sectioncontrol circuit and software modules are designed +e flycontrol system can get the gyroscope data in the flappingwing and receive the operatorrsquos command via Bluetooth Inthe fifth section hovering experiments are conducted andanalyzed to verify the flight performance Finally conclu-sions of this article are presented in the sixth section

2 Structure Design of X-Shaped Flapping-Wing Drone

Many flapping wings use double-bar wing (Figure 4) [56]Since the left wing and right wing do not use the same barthere should be other components to connect the left bar andright bar +is will increase the weight We designed a newsingle-bar wing (Figure 5) +e wings were improved fromdouble-bar to single-bar simplifying the structure and en-hancing the strength +e two pairs of wings of the newX-wing ornithopter are arranged in an X-shaped cross usingtwo single-bar wings with a total of four wings By doingthis we can simplify the flapping support structure

+e ornithopter is composed of gearbox tail fin bodyframe and control system as shown in Figure 6

21 Gearbox Figure 7 illustrates the gearbox structurecomposition +e gearbox is an important mechanism toreduce the speed of the motor increase the torque of themotor and convert the rotary motion of the motor into thereciprocating flapping motion of the wings When thebrushless motor rotates it drives the swing arm gear torotate via the two-stage reduction of the motor gear and themiddle gear +e two swing arm gears mesh with each otherto realize the transmission of power from the right swingarm gear to the left +e swing arm gear drives the eccentriccam to rotate+e eccentric cam drives the tie rod to turn therotary motion into a reciprocating motion of the tie rod+etie rod then drives the elastic support on the wings to swingup and down through the small lifting lugs to achieveflapping motion +e elastic support and the body frame areconnected through an elastic hinge to achieve both rotationrestraint and certain energy recovery +e entire gearboxsystem is fixed on the body frame through a gearbox plate

In this way the gearbox plate the eccentric cam the tierod and the elastic support constitute a crank rockermechanism as shown in Figure 8 By optimizing the size ofeach component on the premise that the optimal workingrange (speed torque) of the motor and the flapping fre-quency of the wings are met the angle range of the elasticsupport movement can be controlled When the amplitudeof the elastic support is 5432deg the angle between the upperand lower wings is maximized when the wings are deployedIt reaches 1115deg+eminimum angle between the upper andlower wings is 286deg when the wings are folded together+eyboth meet the requirements of wing motion amplitudeFigure 8 shows the curve of the wing angle with time whenthe wings are flapped up and down after optimization

22 Tail Fin Figure 6 illustrates the tail fin structure com-position +e tail fin is an important part of controlling theflying pose of the flapping-wing drone Its main function is tocontrol the angle of the rudder wing and the elevator wing

Double-bar

Figure 4 Double-bar wing

Twosingle-bar

Figure 5 Single-bar wing

Journal of Robotics 3

through the servomotor and then change the pitching and left-right flight direction of the flapping-wing drone +e tail fin ismainly composed of a tail fixed bracket a cross-directionalstabilizer a rudder an elevator a rudder wing an elevatorwing a rudder swing arm and a reinforced carbon fiber rodWhen the flapping-wing machine needs to change the di-rection of the pitching motion the rudder (or elevator) willdrive the swing arm Since the swing arm and the rudder wing(or the elevator wing) are fixed together the swing arm of theservo will drive the rudder wing (or the elevator wing) to rotatearound the connection axle between the stabilizer wing and therudder wing (or the elevator wing)+en the drone will changethe direction of the airflow flowing through the tail fin andrealize the change of the direction of the flapping-wing drone

23 Body Frame +e body frame is a rod-shaped structurewith a rectangular cross section and its main function is tofix the entire structural assembly of the flapping-wing drone

Since carbon fiber has the lightest mass among the materialsthat can be selected with the same strength and stiffness thecarbon fiber material is selected as the body material

3 Control Theory

31 Body Dynamics +e positive directions of the coordi-nates are displayed in Figure 9+e x-axis is perpendicular tothe flapping-wing surface and points forward the y-axis ispointing to the left of the flapping-wing drone and the z-axisis vertically upward +e dynamics of the ornithopter can bedescribed under rigid body assumption by NewtonndashEulermotion equations Similar to a drone we obtain 12 ordinarydifferential equations with 12 unknown coordinates velocity(u v w) angular velocity (p q r) position (x y z) andorientation expressed by Roll-Pitch-Yaw angles (φ θ δ) byomitting the equations for position and heading (yaw)[20 57ndash59]

Control system

Brushless motor drive moduleLi battery

GyroscopeWireless communication module

Control module

Tail fin

Tail fixed bracket

Rudder

Servo swing armRudder wing

GearboxBody frame

Wing

Cross-directional stabilizer

Elevator

Reinforced carbon fiber rod

Elevator wing

Single-bar

Figure 6 +e overall structure of the X-shaped ornithopter


Body frame

Gearbox plate

Brushlessmotor

Middle gear

Small lifting lug

Elastic supportElastic hinge

Tie rod

Eccentric CAM

Swing arm gear

(a)

Tie rod

Eccentric CAM

Swing arm gear

Motor gear

Middle gear

Elastic hinge

Body frame

Gearbox plate

Brushless motor

Elastic support Small lifting lug

(b)

Figure 7 Gearbox structure composition (a) Gearbox isometric view (b) Gearbox side view

Elastic support

Tie rod

Eccentric CAM

Gearbox plate

5432deg

(a)

0 2 4 6 8 10 12Time (s)

Ang

le (d

egre

es)

ndash20

0

20

40

60

80

100

120

(b)

Figure 8 (a) Crank rocker mechanism and (b) the curve of the angle between the upper and lower wings with time when the wings areflapped up and down after optimization

x

u

y

v

w

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFly

lR

z

(a)

x

y

z

Yaw

Roll

θRud

(b)

x

y

Pitch

θEle

z

(c)

Figure 9 Continued


+e system is reduced to 8 equations

_u minus (wp minus vr) +X

m+ g sin θ

_v minus (ur minus wp) +Y

mminus g cos θ sinφ

_w minus (vp minus uq) +Z

mminus g cos θ cosφ

Ixx_p Iyy minus Izz1113872 1113873qr + Ixz( _r + pq) + L

Iyy _q Izz minus Ixx( 1113857pr + Ixz r2

minus p2

1113872 1113873 + M

Izz _r Ixx minus Iyy1113872 1113873pq + Ixz( _p + qr) + N

_φ p + q sinφ tan θ + r cosφ tan θ

_θ q cosφ minus r sinφ

(1)

Here m is the body mass and Ixx Iyy Izz and Ixz areboth nonzero moments and product of inertia in body frame(products Ixy and Iyz are both zero due to body symmetry)Aerodynamic forces and moments are represented by vec-tors (X Y Z) and (L M N) respectively [60ndash62]

+e wing forces and tail fin forces are transformed intothe body frame as follows

X FFly sin θFlyxz + FEle

Y FFly sin θFlyyz + FRud

Z FFly cos θFly minus G

L FRudlE

M minus FElelE

FRud 12ρV

2SWRCYθRudθRud

FEle 12ρV

2SWECYθEleθEle

(2)

Here FFly is the drag force produced by flapping wingsθFly is the angle between FFly and z-axis θFlyxz and θFlyyz arethe projection of angle θFly on x-z plane and y-z planerespectively FRud and FEle are the rudder force and elevatorforce produced by rudder wings and elevator wings re-spectively lE is the projection of the distance the tail fin andthe center of gravity of the ornithopter onto the z-axis ρ isair density V is airflow velocity SWR and SWE are the area ofthe rudder wings and elevator wings respectively CYθRud andCYθEle are the rudder lateral force derivative and the elevatorlongitudinal force derivative and θRud and θEle are therudder and elevator rotation angles respectively

Since the rudder wing of the T-shaped tail fin is notplane-symmetrical about y-z surface the flapping wing ofT-shaped tail fin has one more N torque than the cross-shaped tail fin

x

u

y

v

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFlyzw

(d)

x

y

z

O

Roll

θRud

(e)

x

y

z

Pitch

θEle

(f )

Figure 9 +e positive directions of the coordinates and control mechanism (a) dynamic analysis of T-shaped tail fin (b) roll-control andyaw-control by moving the rudder wing (c) pitch-control by moving the elevator wing (d) dynamic analysis of cross-shaped tail fin (e) roll-control by moving the rudder wing and (f) pitch-control by moving the elevator wing


N minus FRudlR (3)

Here lR is the projection of the distance between FRudand the center of gravity of the ornithopter onto the y-axis

SoN torque will cause hovering flapping-wing extra yawmovement of the T-shaped tail fin It should be compensatedby appropriate control mechanism Hence the flapping wingof the cross-shaped tail fin will hover in a more controllablemanner than the T-shaped tail fin because its rudder wing isplane-symmetrical about y-z surface

From these equations we can see that the flapping-wingposture can be controlled by the rudder rotation angles θRudand elevator rotation angles θEle

Figure 9 also shows the control mechanism integrated inour present flapping wing when the rudder wing is movedby a rudder servo as shown in Figures 9(b) and 9(e) theornithopter will create a rolling moment to rotate about thex-axis +e T-shaped ornithopter will also create a yawingmoment to rotate about the z-axis Similarly when the el-evator wing is moved by an elevator servo as shown inFigures 9(c) and 9(f) the ornithopter will create a pitchingmoment to rotate about the y-axis +e two degrees ofcontrol allow us to effectively control the ornithopter

+erefore if we want the ornithopter to have a goodhover flight performance the tail fin must be symmetricalabout the longitudinal axis (z-axis) of the ornithopter

32 Control Strategy +e servo output off-angle position is

Pout KpΔA + Kd

dΔA

dt+ Ki 1113946ΔAdt

ΔA TA minus ActA

(4)

Here Kp Kd and Ki are the parameters of the PIDrespectively TA and ActA are the target posture angle from aremote control and actual posture angle from a gyroscope

+e gyroscope can output precise angle velocity so it isunnecessary to derive ΔA in single-chip microcomputerthen

dΔA

dt minus

dActA

dt minus Actω (5)

Here Actω are actual posture angle velocity fromgyroscope

So the servo output off-angle position changes to

Pout KpΔA minus KdActω + Ki 1113946ΔAdt (6)

By doing this the requirements for the control systemcan be decreased It can improve PID strategy speed And thehovering can be controlled better

Since the servo position is 90 when the flapping wing inhover balance the new servo position after PID beingcontrolled is

P 90 + Pout (7)

According to the signal from a gyroscope and remotecontrol we can calculate the new rudder servo position and

elevator servo position respectively By using this strategywe can control the ornithopter hovering Currently there isno control over the yaw axis which is passively stable byadjusting the fixed angle of two elevator wings manuallyBecause if we control the yaw we will need two servos toadjust two elevator wings respectively not one currently+is will add weight to the flapping wing and make it flydifficultly

4 Control System

41 Flying System Hardware +e control system mainlyconsists of a control module a brushless motor drive module(BMDM) a wireless communication module a gyroscopeand a lithium battery as shown in Figure 6

+e control module uses Beetle single-chip microcom-puter as the core control board It can receive the targetcontrol instructions from the remote control via the Blue-tooth wireless module and then generates a PWM signalbased on the actual posture of the flapping-wing machinedetected by a gyroscope +e PWM signal can control theservo to dynamically adjust the position of the tail fin AndBeetle also generates a PWM signal to control the speed ofthe brushless motor so the flapping frequency of wings canbe controlled

Because the flapping-wing machine is very small involume and mass to ensure the life of the motor and meetthe requirements of powerndashvolume ratio and powerndashmassratio brushless motors and corresponding drive modulesare selected here to realize the rotary drive of the flappingwing Here we use Hobby King AP-03 7000 kV BrushlessMicro Motor (31 g) Table 1 illustrates the parameters of thebrushless motor

+e wireless communication module is mainly used forreceiving the instructions of the remote control andtransmitting them to the control unit to realize the con-trollable flight of the flapping-wing drone To save powerand reduce the volume the Bluetooth 40 BLE module ofCypressrsquos CYBL series chip is selected here It can not onlysave power but also simplify the wiring and programming ofthe main control module by using the serial communicationinterface protocol

+e gyroscope is used to detect the posture of the or-nithopter in real time We use the GY 901 chip It uses anMPU6050 electronic gyroscope chip with a built-in Kalmanfilter algorithm It can output various motion state pa-rameters of the ornithopter in real time such as angleangular velocity and linear velocity

+e lithium battery is 37 V 70mAh which can extendthe flight time as much as possible without increasing toomuch weight of the drone

+e total weight of the system is 1779 g and each part ofthe system is shown in Figure 10 +e hardware circuitconnection is shown in Figure 11 Figure 12 illustrates theornithopter control system and remote control prototype

42 Flying System Software +e system control program ismainly composed of the initialization subprogram wireless


communication subprogram posture control subprogramand execution subprogram +e control block diagram isshown in Figure 13

(1) Initialization Subprogram +e initialization moduleincludes the initialization of the correspondingGPIO port and the initialization of the Bluetoothserial communication (setting the Bluetooth pairingand the communication baud rate of 115200)

(2) Wireless Communication Subprogram +is modulecan determine the order and position of the com-munication instructions according to the keywordsection of the wireless communication +en it canextract the corresponding control instructions (fly-ing speed forward left and right steering) and checkthe last digit to ensure the accuracy of thecommunication

(3) Posture Control Subprogram +is module can readthe information of the gyroscope to get the currentposture of the ornithopter and compare it with thetarget flight posture received from the remote con-troller Based on the PID control algorithm it cancontrol the action of servos to adjust the flightposture

(4) Execution Subprogram +is module can receive thecontrol instructions obtained by the control algo-rithm and convert them into corresponding PWMsignals to control the actions of the brushless motorand servos to complete the execution of the actions

5 Flapping-Wing DroneExperimental Verification

To verify the structural performance and flight controleffect of the designed flapping-wing drone two flapping-wing drone prototypes were produced One has a T-shapedtail fin as shown in Figure 14 and is only controlledmanually Another is controlled by PID strategy and has across-directional tail fin as shown in Figure 12 +ey bothperformed a vertical flight test as shown in Figures 15 and16 to simulate the hummingbirdsrsquo hovering as shown inFigure 1

In supplemental files T-shape Tail Flight Testmp4 isthe flight test video of T-shaped tail fin and Cross Tail FlyFromTablemp4 is the flight test video of cross-shapedtail fin

It can be seen that the ornithopter without control has alarger swing angle than the ornithopter with control +eornithopter without control has also more lateral dis-placement and less hovering time +e hovering time of theornithopter without control is 69s and the hovering timewith control is 15s Moreover there is a more obvious spinflight in the T-shaped flapping-wing drone +is is com-pletely consistent with the previous analysis

It can be seen from Figures 16ndash18 that the ornithopterwith a control system can hover frequently in a fixed areaFigure 19 shows the angle between the body frame andplumb line +e change frequency of the angle of the cross-shaped tail is higher than that of the T-shaped tail and theamplitude is smaller than that of the T-shaped tail +isindicates that the improved PID strategy can adjust timelythe ornithopter posture to hold hovering

Table 1 Parameters of the 7000 kV brushless micro motor

kV (rpmv) 7000Weight (g) 31Max current (A) 4Resistance (mH) 0Max voltage (V) 4LiPo range 1S 37 VVoltage (V) (recommended) 37Current (A) (recommended) 21

Bluetoothmodule063 4

Battery525 29

Brushless motor drive module (BMDM) 076 4

Wires575 32

Beetle 134 8

Gyroscope066 4

Two servos 34

19

Figure 10 +e weight of every part +e total weight is 1779 g

BMDM

S B+

B+TX

TX

Gyro

Bndash

Bndash

B+

B+B+

SCL(D2) SDA(D3) Bndash

BndashBndash

Bndash

Bluetooth moduleRudder Elevator

D10D9RX(D0)

D13

1k

047k

RX

USB

TX(D1) D11

S B+ BndashS

Figure 11 Hardware circuit connection diagram


Since the spin flight or yaw in the T-shaped flapping-wing drone is more obvious than that of the cross-shapedone Moreover the improved PID strategy can only adjustthe ornithopter pitch and roll to hold hovering and does notcontrol yaw So the cross-shaped tail fin is better than theT-shaped one from the perspective of spin flight

+ey also indicate that the designed remote controlsystem and flight control system can achieve a better flighteffect in ornithopterrsquos pitch and roll

At the same time the flapping-wing drone has a largeupward flight acceleration which proves that the developedflapping-wing drone has a large liftndashmass ratio And

Bluetooth module Beetle

Gyroscope

Bluetooth remote control

Figure 12 +e ornithopter control system and remote control prototype

Wireless communication subprogram

Read the first three bytes of the serial port

Right

YRead the last byte of the serial port

N

Right

Y

N

Extract the control instructions

Posture control subprogram

Read gyroscope signal

Calculate posture of the ornithopter Target flight posture

Ornithopters posture PID control algorithm

Instructions from remote controller

Output control instructions

Execution subprogram

Convert into PWM signals

Is the range ofcontrol

instructions right

Y

N

Ruder Elevator BMDM

Starting

Initialization subprogram

GPIO initialization

Bluetooth pairing

Set communication baud rate

Figure 13 +e ornithopter control block diagram


flapping-wing drone can simulate hummingbirds to achievea certain hover flight

However it can be seen from Figures 17ndash19 that the tailalso sways and there is a little spin flight in the flapping-wing drone +erefore further measures need to be taken toensure a well controllable flight

6 Conclusions

In this research a new X-shaped flapping-wing drone wasproposed and the specific mechanism of each part of theflapping-wing drone was designed and analyzed+e controlmechanism of T-shaped and cross-shaped tail fin of flapping

Figure 14 A T-shaped tail fin

0008

12 16

21

27

3032

39

53

58 70

Figure 15 T-shaped tail fin flapping-wing flight without control

290

38 43 105

115

68

77

128

149

Figure 16 Cross-shaped tail fin flapping-wing flight with control

0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)

Not controlledControlled

Figure 17 Flight trajectory of two flapping-wing drones

ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)


Figure 18 Flight trajectory of two flapping-wing drones alongtime

ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)

T-shaped not controlledCross-shaped controlled

Figure 19 Posture angle curve of flight posture


wing was analyzed At the same time to realize the con-trollable flight of the flapping-wing drone a correspondingremote control and flight control system was developed +ehardware circuit and control algorithm were compiled andtwo actual flapping-wing drones were produced and flightexperiments were carried out

+e experimental results show that the designed flap-ping-wing drone has a large liftndashmass ratio and good ma-neuverability +e developed control system and controlmethod can realize the controllable flight of flapping-wingdrone and lay the foundation for future research +e cross-shaped tail fin is better than the T-shaped tail fin in yaw-controlling performance +e cross-shaped tail fin has abetter controllable hovering performance than the T-shapetail fin

In the next stage this study will focus on the spin flightand flight stability of the flapping-wing drone and furthercorrect it through structural improvements and algorithmimprovements to achieve good flapping-wing flight control

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

+is work was supported by the National Natural ScienceFoundation of China (no 51005128) 2018 Teaching Re-search and Teaching Reform Project of Qingdao Universityof Technology (no F2018-113) and 2019 Teaching Researchand Teaching Reform Project of Qingdao University ofTechnology (no F2019-056)

Supplementary Materials

T-shape Tail Flight Testmp4 is the flight test video ofT-shaped tail fin In this video the flapping-wing drone has aT-shaped tail fin and is only controlled manually Cross TailFly FromTablemp4 is the flight test video of the cross-shapedtail fin +e flapping-wing drone is controlled by PID strategyand has a cross-directional tail fin Both flapping-wing dronesare the same except the tail fin (Supplementary Materials)

References

[1] EW Hawkes and D Lentink ldquoFruit fly scale robots can hoverlonger with flapping wings than with spinning wingsrdquo Journalof Ae Royal Society Interface vol 13 pp 1ndash6 2016

[2] C Kang andW Shyy ldquoAnalytical model for instantaneous liftand shape deformation of an insect-scale flapping wing inhoverrdquo Journal of the Royal Society Interface vol 11 pp 1ndash102014

[3] Y Nan K Matej L Mohamed Esseghir and P AndreldquoExperimental optimization of wing shape for a

hummingbird-like flapping wing micro air vehiclerdquo Bio-inspiration amp Biomimetics vol 12 2017

[4] S Chen H Li S Guo M Tong and B Ji ldquoUnsteady aero-dynamic model of flexible flapping wingrdquo Aerospace Scienceand Technology vol 80 pp 354ndash367 2018

[5] P Deshpande and A Modani ldquoExperimental investigation offluid-structure interaction in a bird-like flapping wingrdquoJournal of Fluids and Structures vol 91 p 102712 2019

[6] L Wang and F-B Tian ldquoNumerical study of flexible flappingwings with an immersed boundary method fluid-structure-acoustics interactionrdquo Journal of Fluids and Structures vol 90pp 396ndash409 2019

[7] S Deng J Wang and H Liu ldquoExperimental study of a bio-inspired flapping wing MAV by means of force and PIVmeasurementsrdquo Aerospace Science and Technology vol 94p 105382 2019

[8] J Zhu and J Zhang ldquoPower extraction performance of twosemi-active flapping airfoils at biplane configurationrdquo Journalof Mechanical Science and Technology vol 34 no 1pp 175ndash187 2020

[9] K Stowers Amanda and L David ldquoFolding in and out passivemorphing in flapping wingsrdquo Bioinspiration amp Biomimeticsvol 10 2015

[10] D Faux O +omas S Grondel and E Cattan ldquoDynamicsimulation and optimization of artificial insect-sized flappingwings for a bioinspired kinematics using a two resonant vi-bration modes combinationrdquo Journal of Sound and Vibrationvol 460 p 114883 2019

[11] M Huang ldquoOptimization of flapping wing mechanism ofbionic eaglerdquo Proceedings of the Institution of MechanicalEngineers vol 33 pp 3261ndash3272 2019

[12] M Hassanalian and A Abdelkefi ldquoTowards improved hybridactuation mechanisms for flapping wing micro air vehiclesanalytical and experimental investigationsrdquo Drones vol 3no 3 p 73 2019

[13] C Chen and T Zhang ldquoA review of design and fabrication ofthe bionic flapping wing micro air vehiclesrdquo Micromachinesvol 10 pp 1ndash20 2019

[14] M Keennon K Klingebiel and HWon ldquoDevelopment of thenano hummingbird a tailless flapping wing micro air vehi-clerdquo in Proceedings of the 50th AIAA Aerospace SciencesMeeting p 588 Simi Valley CA USA January 2012

[15] Q V Nguyen H C Park N S Goo and D Byun ldquoChar-acteristics of a beetlersquos free flight and a flapping-wing systemthat mimics beetle flightrdquo Journal of Bionic Engineering vol 7no 1 pp 77ndash86 2010

[16] N Gaissert R Mugrauer G Mugrauer A Jebens K Jebensand E M Knubben ldquoInventing a micro aerial vehicle inspiredby the mechanics of dragonfly flightrdquo in Towards AutonomousRobotic Systems pp 90ndash100 Springer Berlin Germany 2013

[17] G Gremillion P Samuel and J S Humbert ldquoYaw feedbackcontrol of a bio-inspired flapping wing vehiclerdquo inMicro-andNanotechnology Sensors Systems and Applications IV In-ternational Society for Optics and Photonics BellinghamWA USA 2012

[18] D Coleman M Benedict V Hrishikeshavan and I ChopraldquoDesign development and flight-testing of a robotic hum-mingbirdrdquo in Proceedings of the 71st Annual Forum of theAmerican Helicopter Society Virginia Beach VA USA May2015

[19] H V Phan S Aurecianus T Kang and H C Park ldquoAttitudecontrol mechanism in an insect-like tailless two-winged flyingrobot by simultaneous modulation of stroke plane and wingtwistrdquo in Proceedings of the International Micro Air Vehicle


Conference and Competition Melbourne Australia Septem-ber 2018

[20] A Roshanbin H Altartouri M Karasek and A PreumontldquoCOLIBRI a hovering flapping twin-wing robotrdquo Interna-tional Journal of Micro Air Vehicles vol 9 no 4 pp 270ndash2822017

[21] J Zhang F Fei Z Tu and X Deng ldquoDesign optimization andsystem integration of robotic hummingbirdrdquo in Proceedings ofthe 2017 IEEE International Conference on Robotics andAutomation (ICRA) pp 5422ndash5428 10 Bayfront AvenueSigapore June 2017

[22] C De Wagter M Karasek and G de Croon ldquoQuad-thoptertailless flapping wing robot with four pairs of wingsrdquo Inter-national Journal of Micro Air Vehicles vol 10 no 3pp 244ndash253 2018

[23] Q V Nguyen and W L Chan ldquoDevelopment and flightperformance of a biologically-inspired tailless flapping-wingmicro air vehicle with wing stroke plane modulationrdquo Bio-inspiration amp Biomimetics vol 14 2018

[24] M Karasek F T Muijres C DeWagter B D W Remes andG C H E de Croon ldquoA tailless aerial robotic flapper revealsthat flies use torque coupling in rapid banked turnsrdquo Sciencevol 361 no 6407 pp 1089ndash1094 2018

[25] X Chi S Wang Y Zhang X Wang and Q Guo ldquoA taillessbutterfly-type ornithopter with low aspect ratio wingsrdquo inProceedings of the CSAAIET International Conference onAircraft Utility Systems Guiyang China June 2018

[26] M Keennon and J Grasmeyer ldquoDevelopment of two MAVsand vision of the future of MAV designrdquo in Proceedings of theAIAA International Air and Space Symposium and ExpositionAe Next 100 Years p 2901 Simi Valley CA USA July 2003

[27] J H Park and K-J Yoon ldquoDesigning a biomimetic orni-thopter capable of sustained and controlled flightrdquo Journal ofBionic Engineering vol 5 no 1 pp 39ndash47 2008

[28] C De Wagter S Tijmons B D Remes and G C de CroonldquoAutonomous flight of a 20- gram flapping wing mav with a 4-gram onboard stereo vision systemrdquo in Proceedings of the 2014IEEE International Conference on Robotics and Automationpp 4982ndash4987 Hong Kong China May 2014

[29] W Send M Fischer K Jebens R MugrauerA Nagarathinam and F Scharstein ldquoArtificial hinged-wingbird with active torsion and partially linear kinematicsrdquo inProceeding of 28th Congress of the International Council of theAeronautical Sciences Brisbane Australia September 2012

[30] A E Holness H A Bruck and S K Gupta ldquoCharacterizingand modeling the enhancement of lift and payload capacityresulting from thrust augmentation in a propeller-assistedflapping wing air vehiclerdquo International Journal of Micro AirVehicles vol 10 no 1 pp 50ndash69 2018

[31] C Rose and R S Fearing ldquoComparison of ornithopter windtunnel force measurements with free flightrdquo in Proceeding ofthe 2014 IEEE International Conference on Robotics andAutomation pp 1816ndash1821 Hong Kong China June 2014

[32] G A Folkertsma W Straatman N Nijenhuis C H Vennerand S Stramigioli ldquoRobird a robotic bird of preyrdquo IEEERobotics amp Automation Magazine vol 24 no 3 pp 22ndash292017

[33] M H Rosen G le Pivain R Sahai N T Jafferis andR J Wood ldquoDevelopment of a 32 g untethered flapping-wingplatform for flight energetics and control experimentsrdquo inProceedings of the 2016 IEEE International Conference onRobotics and Automation pp 3227ndash3233 Stockholm Swe-den May 2016

[34] M Ghommem M Hassanalian M Al-MarzooqiG +roneberry and A Abdelkefi ldquoSizing process aerody-namic analysis and experimental assessment of a biplaneflapping wing nano air vehiclerdquo Proceedings of the Institutionof Mechanical Engineers Part G Journal of Aerospace Engi-neering vol 233 no 15 pp 5618ndash5636 2019

[35] M Hassanalian and A Abdelkefi ldquoClassifications applica-tions and design challenges of drones a reviewrdquo Progress inAerospace Sciences vol 91 pp 99ndash131 2017

[36] A Shahzad F-B Tian J Young J C S Lai and S LaildquoEffects of flexibility on the hovering performance of flappingwings with different shapes and aspect ratiosrdquo Journal ofFluids and Structures vol 81 pp 69ndash96 2018

[37] T Nakata and H Liu ldquoAerodynamic performance of ahovering hawkmoth with flexible wings a computationalapproachrdquo Proceedings of the Royal Society B BiologicalSciences vol 279 pp 722ndash731 2012

[38] H Vu Phan T K L Au and H C Park ldquoClap-and-lingmechanism in a hovering insect-like two-winged lapping-wing micro air vehiclerdquo Royal Society Open Science vol 3pp 160746ndash162016 2016

[39] B Singh M Ramasamy I Chopra and J Leishman ldquoEx-perimental studies on insect-based flapping wings for microhovering air vehiclesrdquo in Proceedings of the 46th AIAAASMEASCEAHSASC Structures Structural Dynamics and Mate-rials Conference p 2293 College Park MD USA April 2005

[40] K Mazaheri and A Ebrahimi ldquoExperimental investigation ofthe effect of chordwise flexibility on the aerodynamics offlapping wings in hovering flight flexibility on the aerody-namics of flapping wings in hovering flightrdquo Journal of Fluidsand Structures vol 26 no 4 pp 544ndash558 2010

[41] K De Clercq R De Kat B Remes et al ldquoFlow Visualizationand Force Measurements on a Hovering Flapping-WingMAV ldquoDelFly IIrdquordquo in Proceedings of the 39th AIAA FluidDynamics Conference p 4035 San Antonio TX USA June2009

[42] Q V Nguyen W L Chan and M Debiasi ldquoExperimentalinvestigation of wing flexibility on force generation of ahovering flapping wing micro air vehicle with double wingclap-and-fling effectsrdquo International Journal of Micro AirVehicles vol 9 no 3 pp 187ndash197 2017

[43] T Jiang X Yang H Wang W Gai and L Cui ldquoLongitudinalmodeling and control of tailed flapping-wings micro air ve-hicles near hoveringrdquo Journal of Robotics vol 2019 Article ID9341012 12 pages 2019

[44] H E Taha S Tahmasian C A Woolsey A H Nayfeh andM R Hajj ldquo+e need for higher-order averaging in thestability analysis of hovering flapping-wing flightrdquo Bio-inspiration amp Biomimetics vol 10 2015

[45] B Cheng and X Deng ldquoTranslational and rotational dampingof flapping flight and its dynamics and stability at hoveringrdquoIEEE Transactions on Robotics vol 27 no 5 pp 849ndash8642011

[46] P Chirarattananon K Y Ma and R J Wood ldquoAdaptivecontrol of a millimeter-scale flapping-wing robotrdquo Bio-inspiration amp Biomimetics vol 9 pp 1ndash15 2014

[47] H Altartouri A Roshanbin G Andreolli et al ldquoPassivestability enhancement with sails of a hovering flapping twin-wing robotrdquo International Journal of Micro Air Vehiclesvol 11 pp 1ndash9 2019

[48] S C Taylor S Ferrari S B Fuller and R J Wood ldquoSpikingNeural Network (SNN) control of a flapping insect-scalerobotrdquo in Proceedings of the IEEE 55th Conference on Decision


and Control pp 3381ndash3388 Las Vegas NV USA December2016

[49] E B James C-K Kang and Y Shtessel ldquoControl of aflapping-wing micro air vehicle sliding-mode approachrdquoJournal of Guidance Control and Dynamics vol 41pp 1223ndash1226 2018

[50] J E Bluman C-K Kang and Y B Shtessel ldquoSliding modecontrol of a biomimetic flapping wing micro air vehicle inhoverrdquo in Proceedings of the AIAA Atmospheric Flight Me-chanics Conference p 1633 Grapevine TX USA January2017

[51] Perez-Arancibia O Nestor J P Whitney and R J WoodldquoLift force control of flapping-wing microrobots usingadaptive feedforward schemesrdquo IEEEASME Transactions onMechatronics vol 18 pp 155ndash168 2013

[52] S Mishra B Tripathi S Garg A Kumar and P KumarldquoDesign and development of a bio-inspired flapping wing typemicro air vehiclerdquo Procedia Materials Science vol 10pp 519ndash526 2015

[53] Y Peng J Cao L Liu and H Yu ldquoA piezo-driven flappingwing mechanism for micro air vehiclesrdquo Microsystem Tech-nologies vol 23 no 4 pp 967ndash973 2017

[54] S Yoon L-H Kang and S Jo ldquoDevelopment of air vehiclewith active flapping and twisting of wingrdquo Journal of BionicEngineering vol 8 no 1 pp 1ndash9 2011

[55] P S Sreetharan and R J Wood ldquoPassive torque regulation inan underactuated flapping wing robotic insectrdquo AutonomousRobots vol 31 no 2-3 pp 225ndash234 2011

[56] B H Cheaw H W Ho and E Abu Bakar ldquoWing designfabrication and analysis for an X-wing flapping-wing microair vehiclerdquo Drones vol 3 no 3 p 65 2019

[57] M Karasek Robotic hummingbird design of a controlmechanism for a hovering flapping wing micro air vehiclePhD thesis Universite Libre de Bruxelles Bruxelles Bel-gium 2014

[58] W Su and C Cesnik ldquoFlight dynamic stability of a flappingwing micro air vehicle in hoverrdquo in Proceedings of the 52ndAIAAASMEASCEAHSASC Structures Structural Dy-namics and Materials Conference vol 13 Ann Arbor MIUSA April 2011

[59] H E Taha M R Hajj and A H Nayfeh ldquoWing kinematicsoptimization for hovering micro air vehicles using calculus ofvariationrdquo Journal of Aircraft vol 50 no 2 pp 610ndash614 2013

[60] M Karasek A Hua Y Nan M Lalami and A PreumontldquoPitch and roll control mechanism for a hovering flappingwing MAVrdquo International Journal of Micro Air Vehiclesvol 6 no 4 pp 253ndash264 2014

[61] P E J Duhamel C O Perez-Arancibia G L Barrows andR J Wood ldquoBiologically inspired optical-flow sensing foraltitude control of flapping-wing microrobotsrdquo IEEEASMETransactions on Mechatronics vol 18 pp 556ndash568 2013

[62] C Badrya B Govindarajan J D Baeder A Harrington andC M Kroninger ldquoComputational and experimental inves-tigation of a flapping-wing micro air vehicle in hoverrdquo Journalof Aircraft vol 56 no 4 pp 1610ndash1625 2019


Figure 1 Hummingbirds can hover easily by changing the angle and shape of their wings and tail fin

(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k) (l)

Figure 2 Motor-driven insect-inspired tailless FWMAVs capable of free controlled flying (a) Nano Hummingbird developed by Aer-oVironment Inc [14] (b) TechJect Dragonfly developed by TechJect Inc [15] (c) BionicOpter developed by Festo AG amp Co KG [16] (d)eMotionButterflies developed by Festo AG amp Co KG [17] (e) Robotic Hummingbird developed by Texas AampM University [18] (f )KUBeetle developed by Konkuk University [19] (g) Colibri robot developed by the Universite Libre de Bruxelles [20] (h) RoboticHummingbird developed by Purdue University [21] (i) Quad-thopter developed by Delft University of Technology [22] (j) NUS-Robobirddeveloped by the National University of Singapore [23] (k) DelFly Nimble developed by the Delft University of Technology [24] (l)Butterfly-type ornithopter developed by Beihang University [25]

(a) (b) (c) (d)

(e) (f ) (g) (h)

(i) (j) (k) (l)

Figure 3 Examples of existing bird-inspired tailed FWAVs (a) Microbat from AeroVironment Inc [26] (b) 32 g ornithopter from KonkukUniversity [27] (c) DelFly Explorer from the Delft University of Technology [28] (d) SmartBird from Festo AG amp Co KG [29] (e) RoboRaven V from the University of Maryland [30] (f ) H2Bird ornithopter from the University of California Berkeley [31] (g) Robird fromClear Flight Solutions and the University of Twente [32] (h) BionicBird from httpbionicbirdcom (i) 32 g flapping-wing platform fromHarvard University [33] (j) NAV from the American University of Sharjah [34] (k) Slow Hawk 2 from Kinkade RC (l) Butterflyrsquos spydrone from Israel Aircraft Industries (IAI) [35]













Double-bar


Twosingle-bar






3 Control Theory


Control system



Control module

Tail fin

Tail fixed bracket

Rudder


GearboxBody frame

Wing


Elevator


Elevator wing

Single-bar



Body frame

Gearbox plate

Brushlessmotor

Middle gear

Small lifting lug


Tie rod

Eccentric CAM

Swing arm gear

(a)

Tie rod

Eccentric CAM

Swing arm gear

Motor gear

Middle gear

Elastic hinge

Body frame

Gearbox plate

Brushless motor


(b)


Elastic support

Tie rod

Eccentric CAM

Gearbox plate

5432deg

(a)

0 2 4 6 8 10 12Time (s)

Ang

le (d

egre

es)

ndash20

0

20

40

60

80

100

120

(b)


x

u

y

v

w

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFly

lR

z

(a)

x

y

z

Yaw

Roll

θRud

(b)

x

y

Pitch

θEle

z

(c)

Figure 9 Continued




m+ g sin θ







minus p2

1113872 1113873 + M




(1)






L FRudlE

M minus FElelE

FRud 12ρV

2SWRCYθRudθRud

FEle 12ρV

2SWECYθEleθEle

(2)



x

u

y

v

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFlyzw

(d)

x

y

z

O

Roll

θRud

(e)

x

y

z

Pitch

θEle

(f )



N minus FRudlR (3)







Pout KpΔA + Kd

dΔA

dt+ Ki 1113946ΔAdt

ΔA TA minus ActA

(4)



dΔA

dt minus

dActA

dt minus Actω (5)






P 90 + Pout (7)



4 Control System























Battery525 29


Wires575 32

Beetle 134 8

Gyroscope066 4

Two servos 34

19


BMDM

S B+

B+TX

TX

Gyro

Bndash

Bndash

B+

B+B+


BndashBndash

Bndash


D10D9RX(D0)

D13

1k

047k

RX

USB

TX(D1) D11

S B+ BndashS







Gyroscope





Right


N

Right

Y

N











instructions right

Y

N

Ruder Elevator BMDM

Starting


GPIO initialization

Bluetooth pairing






6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References
















































































Double-bar


Twosingle-bar






3 Control Theory


Control system



Control module

Tail fin

Tail fixed bracket

Rudder


GearboxBody frame

Wing


Elevator


Elevator wing

Single-bar



Body frame

Gearbox plate

Brushlessmotor

Middle gear

Small lifting lug


Tie rod

Eccentric CAM

Swing arm gear

(a)

Tie rod

Eccentric CAM

Swing arm gear

Motor gear

Middle gear

Elastic hinge

Body frame

Gearbox plate

Brushless motor


(b)


Elastic support

Tie rod

Eccentric CAM

Gearbox plate

5432deg

(a)

0 2 4 6 8 10 12Time (s)

Ang

le (d

egre

es)

ndash20

0

20

40

60

80

100

120

(b)


x

u

y

v

w

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFly

lR

z

(a)

x

y

z

Yaw

Roll

θRud

(b)

x

y

Pitch

θEle

z

(c)

Figure 9 Continued




m+ g sin θ







minus p2

1113872 1113873 + M




(1)






L FRudlE

M minus FElelE

FRud 12ρV

2SWRCYθRudθRud

FEle 12ρV

2SWECYθEleθEle

(2)



x

u

y

v

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFlyzw

(d)

x

y

z

O

Roll

θRud

(e)

x

y

z

Pitch

θEle

(f )



N minus FRudlR (3)







Pout KpΔA + Kd

dΔA

dt+ Ki 1113946ΔAdt

ΔA TA minus ActA

(4)



dΔA

dt minus

dActA

dt minus Actω (5)






P 90 + Pout (7)



4 Control System























Battery525 29


Wires575 32

Beetle 134 8

Gyroscope066 4

Two servos 34

19


BMDM

S B+

B+TX

TX

Gyro

Bndash

Bndash

B+

B+B+


BndashBndash

Bndash


D10D9RX(D0)

D13

1k

047k

RX

USB

TX(D1) D11

S B+ BndashS







Gyroscope





Right


N

Right

Y

N











instructions right

Y

N

Ruder Elevator BMDM

Starting


GPIO initialization

Bluetooth pairing






6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References








































































3 Control Theory


Control system



Control module

Tail fin

Tail fixed bracket

Rudder


GearboxBody frame

Wing


Elevator


Elevator wing

Single-bar



Body frame

Gearbox plate

Brushlessmotor

Middle gear

Small lifting lug


Tie rod

Eccentric CAM

Swing arm gear

(a)

Tie rod

Eccentric CAM

Swing arm gear

Motor gear

Middle gear

Elastic hinge

Body frame

Gearbox plate

Brushless motor


(b)


Elastic support

Tie rod

Eccentric CAM

Gearbox plate

5432deg

(a)

0 2 4 6 8 10 12Time (s)

Ang

le (d

egre

es)

ndash20

0

20

40

60

80

100

120

(b)


x

u

y

v

w

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFly

lR

z

(a)

x

y

z

Yaw

Roll

θRud

(b)

x

y

Pitch

θEle

z

(c)

Figure 9 Continued




m+ g sin θ







minus p2

1113872 1113873 + M




(1)






L FRudlE

M minus FElelE

FRud 12ρV

2SWRCYθRudθRud

FEle 12ρV

2SWECYθEleθEle

(2)



x

u

y

v

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFlyzw

(d)

x

y

z

O

Roll

θRud

(e)

x

y

z

Pitch

θEle

(f )



N minus FRudlR (3)







Pout KpΔA + Kd

dΔA

dt+ Ki 1113946ΔAdt

ΔA TA minus ActA

(4)



dΔA

dt minus

dActA

dt minus Actω (5)






P 90 + Pout (7)



4 Control System























Battery525 29


Wires575 32

Beetle 134 8

Gyroscope066 4

Two servos 34

19


BMDM

S B+

B+TX

TX

Gyro

Bndash

Bndash

B+

B+B+


BndashBndash

Bndash


D10D9RX(D0)

D13

1k

047k

RX

USB

TX(D1) D11

S B+ BndashS







Gyroscope





Right


N

Right

Y

N











instructions right

Y

N

Ruder Elevator BMDM

Starting


GPIO initialization

Bluetooth pairing






6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References





































































Body frame

Gearbox plate

Brushlessmotor

Middle gear

Small lifting lug


Tie rod

Eccentric CAM

Swing arm gear

(a)

Tie rod

Eccentric CAM

Swing arm gear

Motor gear

Middle gear

Elastic hinge

Body frame

Gearbox plate

Brushless motor


(b)


Elastic support

Tie rod

Eccentric CAM

Gearbox plate

5432deg

(a)

0 2 4 6 8 10 12Time (s)

Ang

le (d

egre

es)

ndash20

0

20

40

60

80

100

120

(b)


x

u

y

v

w

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFly

lR

z

(a)

x

y

z

Yaw

Roll

θRud

(b)

x

y

Pitch

θEle

z

(c)

Figure 9 Continued




m+ g sin θ







minus p2

1113872 1113873 + M




(1)






L FRudlE

M minus FElelE

FRud 12ρV

2SWRCYθRudθRud

FEle 12ρV

2SWECYθEleθEle

(2)



x

u

y

v

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFlyzw

(d)

x

y

z

O

Roll

θRud

(e)

x

y

z

Pitch

θEle

(f )



N minus FRudlR (3)







Pout KpΔA + Kd

dΔA

dt+ Ki 1113946ΔAdt

ΔA TA minus ActA

(4)



dΔA

dt minus

dActA

dt minus Actω (5)






P 90 + Pout (7)



4 Control System























Battery525 29


Wires575 32

Beetle 134 8

Gyroscope066 4

Two servos 34

19


BMDM

S B+

B+TX

TX

Gyro

Bndash

Bndash

B+

B+B+


BndashBndash

Bndash


D10D9RX(D0)

D13

1k

047k

RX

USB

TX(D1) D11

S B+ BndashS







Gyroscope





Right


N

Right

Y

N











instructions right

Y

N

Ruder Elevator BMDM

Starting


GPIO initialization

Bluetooth pairing






6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References







































































m+ g sin θ







minus p2

1113872 1113873 + M




(1)






L FRudlE

M minus FElelE

FRud 12ρV

2SWRCYθRudθRud

FEle 12ρV

2SWECYθEleθEle

(2)



x

u

y

v

YawRoll

Pitch

FRud

FEle

G

FFly

lE

δr Nφ

p L

θq M

θFlyzw

(d)

x

y

z

O

Roll

θRud

(e)

x

y

z

Pitch

θEle

(f )



N minus FRudlR (3)







Pout KpΔA + Kd

dΔA

dt+ Ki 1113946ΔAdt

ΔA TA minus ActA

(4)



dΔA

dt minus

dActA

dt minus Actω (5)






P 90 + Pout (7)



4 Control System























Battery525 29


Wires575 32

Beetle 134 8

Gyroscope066 4

Two servos 34

19


BMDM

S B+

B+TX

TX

Gyro

Bndash

Bndash

B+

B+B+


BndashBndash

Bndash


D10D9RX(D0)

D13

1k

047k

RX

USB

TX(D1) D11

S B+ BndashS







Gyroscope





Right


N

Right

Y

N











instructions right

Y

N

Ruder Elevator BMDM

Starting


GPIO initialization

Bluetooth pairing






6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References





































































N minus FRudlR (3)







Pout KpΔA + Kd

dΔA

dt+ Ki 1113946ΔAdt

ΔA TA minus ActA

(4)



dΔA

dt minus

dActA

dt minus Actω (5)






P 90 + Pout (7)



4 Control System























Battery525 29


Wires575 32

Beetle 134 8

Gyroscope066 4

Two servos 34

19


BMDM

S B+

B+TX

TX

Gyro

Bndash

Bndash

B+

B+B+


BndashBndash

Bndash


D10D9RX(D0)

D13

1k

047k

RX

USB

TX(D1) D11

S B+ BndashS







Gyroscope





Right


N

Right

Y

N











instructions right

Y

N

Ruder Elevator BMDM

Starting


GPIO initialization

Bluetooth pairing






6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References


















































































Battery525 29


Wires575 32

Beetle 134 8

Gyroscope066 4

Two servos 34

19


BMDM

S B+

B+TX

TX

Gyro

Bndash

Bndash

B+

B+B+


BndashBndash

Bndash


D10D9RX(D0)

D13

1k

047k

RX

USB

TX(D1) D11

S B+ BndashS







Gyroscope





Right


N

Right

Y

N











instructions right

Y

N

Ruder Elevator BMDM

Starting


GPIO initialization

Bluetooth pairing






6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References









































































Gyroscope





Right


N

Right

Y

N











instructions right

Y

N

Ruder Elevator BMDM

Starting


GPIO initialization

Bluetooth pairing






6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References







































































6 Conclusions



0008

12 16

21

27

3032

39

53

58 70


290

38 43 105

115

68

77

128

149


0

100

200

300

400

500

600

0 200 400 600

Z (m

m)

X (mm)



ndash200 0 200 400600

0510150

100200300400500600

X (mm)Time (s)

Z (m

m)



ndash20

ndash10

0

10

20

30

40

0 1 2 3 4 5 6 7 8Time (s)

9 10 11 12 13 14 15

Postu

re an

gle (

deg)







Data Availability




Acknowledgments




References








































































Data Availability




Acknowledgments




References





































































Analysis on Hover Control Performance of T- and Cross ...

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