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Mechanical Systemsand

Signal Processing

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Mechanical Systems and Signal Processing 22 (2008) 1304–1315

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Development of a small flapping robotMotion analysis during takeoff by numerical

simulation and experiment

Taro Fujikawaa,�, Kazuaki Hirakawaa, Shinnosuke Okumaa,Takamasa Udagawab, Satoru Nakanoa, Koki Kikuchia

aDepartment of Mechanical Science and Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016, JapanbSEGA Co., Ltd., 1-2-12 Haneda, Ota-ku, Tokyo 144-8531, Japan

Received 7 January 2007; received in revised form 2 December 2007; accepted 21 January 2008

Available online 2 February 2008

Abstract

We present the development of a small flapping robot for use as an observation system in hazardous environments. An

isometric physical model was constructed based on the observations of body and wing motions during takeoff of a

butterfly, and we compared the flapping motion of the model with that of a butterfly. A computational model based on the

finite-element method is used to analyze the vortex around the wing of the model during takeoff of the constructed robot.

Computation results clarify the takeoff mechanism of the model and show the feasibility of a small flying device employing

a flapping mechanism.

r 2008 Elsevier Ltd. All rights reserved.

Keywords: Flapping robot; Butterfly; Takeoff; CFD; FEM

1. Introduction

In this study, we first investigated the structural mechanism of a butterfly and the body and wing motionsduring takeoff using a three-dimensional high-speed camera system. Based on the results, we then constructedan isometric model using the same flapping mechanism and compared the flapping motion with that of abutterfly. Finally, we formulated a method for computing the body motion, the elastic deformation of thewing and the flow field around the wing and analyzed the motion of the constructed model and the vortexaround the wing.

Flying robots offer great promise as observation systems in hazardous environments because they are notaffected by ground conditions [1,2]. Although several flying vehicles with different methods of lift andpropulsion exist, such as jet planes and helicopters, ‘‘flapping’’, as performed by living creatures, offers manyadvantages for the important abilities of being able to turn at nearly right angles and to accelerate to over

e front matter r 2008 Elsevier Ltd. All rights reserved.

ssp.2008.01.008

ing author.

ess: fujikawa.gf0@gs.it-chiba.ac.jp (T. Fujikawa).

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several Gs at the moment of takeoff. The flapping mechanism used by insects is particularly attractive formaneuvering through a narrow space such as a gap between debris. It is generally conceived that flying insectsacquire lift through interaction with the vortex around the wing boundary generated by flapping and,therefore, many researchers have recently been studying this mechanism [3–6]. However, this structure–fluidcoupled problem becomes even more difficult and highly complex when the deformation of elastic wings bythe fluid is introduced and the flow field varies with the wing motion and has not yet been fully solved.

Meanwhile, the ability of insects to control their flight is very high, despite the fact that the number ofneurons in an insect brain is barely of the order of 105. Hence, they must use the characteristics of their bodystructure very effectively, implying that a control system can be simplified by employing the dynamics of thestructural system. The design concept of this study is to adopt the scheme of flying insects where they do notrequire a complicated control system, but instead have structural characteristics with which lift is generatedthrough simple body vibrations, i.e., flapping. In other words, our control system takes full advantage of thestructural characteristics of the robot body. Hence, the essence of the design principle is that the controlsystem and the structural system are in balance. This design principle may be particularly significant formicromachines where high-end CPUs, sensors and actuators are difficult to use.

From the above standpoint, the balanced design and control methods of living creatures have recentlydrawn attention, particularly ‘‘flapping’’ for use in small flying devices [7–10]. Sudo and Tsuyuki [11] haveanalyzed the wing structure and aerodynamic characteristics of dragonflies. Fry et al. [12] have investigatedthe wing and body kinematics of free-flying fruit flies using three-dimensional infrared high-speed video. Thesestudies have shown the importance of the fluid around the wings. However, it is difficult to develop flyingdevices based on a dragonfly, which moves four wings independently and has many degrees of freedom(DOF), or a fly with an mm-order-sized body and a high flapping frequency of around 100Hz. Dickinson et al.[13,14] have constructed model wings of a fly and have clarified the mechanism of lift generation. However,this model cannot be used to analyze the structural characteristics of the wing or the motion properties of thewhole body, because, while the Reynolds number corresponds to that of a fly, the size does not. Similarly,although some researchers [15–17] have developed tiny sensors and actuators for realizing a fly-like flappingrobot, it is extremely difficult to mount actuators of more than 102Hz frequencies on a weight of only 102mg,as well as plural sensors for flight stabilization. In addition, although several large-bird-size robots have beenproduced [18], flapping of these robots is not very efficient and gliding is far more often employed.

From this starting point, we developed a small flapping robot that utilizes the dynamics of its own structuralsystem and a simplified control system. Here we focus on a butterfly with only a few DOF and a low flappingfrequency as a flapping model.

2. Motion analysis of a butterfly

2.1. Experimental setup and specimen

In this study, we use a butterfly as a flapping model and analyze its flight mechanism. Butterfly-style flightrequires a simple control system with effective use of the dynamics of the structural system: the flappingfrequency is low (approximately 10Hz) and the DOF is also low because phases of flapping of the fore- andhind-wings are the same. Here, the following parameters were investigated as defined in Fig. 1: the positionand acceleration of the thorax, the flapping frequency, the stroke of flapping, the stroke of abdomen swing andthe stroke of the pitch angle. A three-dimensional high-speed camera system with a resolution of 640� 480pixels and 200 fps was used for this experiment. The space for the butterfly flight was 900mm� 900mm�900mm.

In this experiment, we photographed takeoff motions of 16 swallowtail butterflies, Papilio xuthus (with anaverage wing span of 125mm, an average forewing length of 69mm and an average mass of 550mg).

2.2. Results and discussion

Fig. 2 shows an example of stroboscopic photographs taken during takeoff of a butterfly using a three-dimensional high-speed camera system. As shown in this figure, the butterfly moved upward during

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xy

z

Stroke of flapping

z

Head

Thorax

Abdomen

Forewing

Flapping angle

Abdomen angle

Hind wing

.

Stroke of abdomen swing

Pitch angle

Fig. 1. Parameter definitions for a butterfly: (a) front view and (b) side view.

Fig. 2. Stroboscopic photographs taken during takeoff of a butterfly.

-90

-75

Time (ms)

-60

-45

-30

-15

00 10 20 30 40 50 60 70 80 90 100 110

Ang

le (

deg) 15

30

45

60

75

90Flapping angleAbdomen anglePitch angle

Fig. 3. An example of relationship among flapping angle, abdomen angle, and pitch angle of a butterfly during takeoff.

T. Fujikawa et al. / Mechanical Systems and Signal Processing 22 (2008) 1304–13151306

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a downstroke and then moved forward during an upstroke. Additionally, the butterfly controlled the pitchangle by swinging its abdomen up during a downstroke, and by swinging it down during an upstroke. Fig. 3shows a typical example of the relationships among the flapping angle, the abdomen angle and the pitch angleduring the first stroke. As shown in this figure, the angles of flapping and abdomen had the same frequencybut were in antiphase. Unlike a dragonfly, a butterfly cannot control its fore- and hind-wings independently,and hence it controls its pitch angle by swinging its abdomen. Fig. 4 displays the trajectory of the thorax centercorresponding to the same first stroke. This trajectory matches the observation that a butterfly flies upward(z-direction) during the downstroke and flies forward (x-direction) during the upstroke. Fig. 5 showsthe acceleration trajectory of the thorax center during the same first stroke. Here vertical and horizontalaxes mean the accelerations for z and x directions, and ‘‘A’’ and ‘‘B’’ correspond to those in Fig. 4. Wefound that there are two points where the acceleration is maximum: the first point (‘‘A’’ in Figs. 4 and 5)is in the z-direction and the second (‘‘B’’ in Figs. 4 and 5) is in the x-direction. Note that the maximumacceleration in this experiment was 5.8G. Then, the average initial angle of flapping was 72.01 (standarddeviation was 12.11) in this experiment, though it is generally shown that the flapping of a butterfly starts fromnearly 901.

A

B

X (mm)

0-5

-20

0

20

40

60

80

-10

Z (

mm

)

5 10 15

Fig. 4. Trajectory of the thorax center of a butterfly during a stroke. ‘‘A’’ is the point of the maximum acceleration during downstroke and

‘‘B’’ is the point of the maximum acceleration during upstroke.

A

B

-14.0x’’ (G)

z’’ (

G)

-12.0

-10.0

-10.0

-8.0

-8.0

-6.0

-6.0

-4.0

-4.0-2.0

-2.00.0

0.0

2.0

2.0

4.0

4.0 6.0 8.0 10.0 12.0

Fig. 5. Acceleration of the thorax center of a butterfly during a stroke. ‘‘A’’ is the point of the maximum acceleration during downstroke

and ‘‘B’’ is the point of the maximum acceleration during upstroke.

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3. Design of a small flapping robot

3.1. Design of hardware

We designed isometric hardware based on the following values obtained in Section 2: wing span of 120mm,stroke of flapping from 601 to �301, stroke of abdomen swing from 101 to �101 (note that flapping frequencydepends on actuator torque and flapping strokes depend on the frequency), mass of 720mg, and flapping andabdomen angles of the same frequency and in antiphase. Also, the leading edge and the anal vein weredesigned to be highly rigid using stiff frames. This hardware employed a rubber motor as an actuator and theposture control was passive. Generally, there are many mechanisms for flapping, for example, J. Yan et al. [19]developed a four-bar mechanism. However, such a mechanism cannot realize the large flapping angle andsimple abdomen swing. Thus, in this study, we employed a slider-clank mechanism for flapping of 1001 andabdomen swing by 1 DOF. As shown in Fig. 6, the crank mechanism translates the rotation of the actuatorinto the flapping of the wing and the up-and-down motion of a connection rod through a slider swings theabdomen. Note that the body part including the crank, the abdomen and the frame of the wings is made ofbamboo, which has high comparable rigidity compared with metals. The wings are made of a thin clear film(a commercial plastic kitchen wrap). Also, the fore- and hind-wings are connected into a single wing and theshape of the trailing edge is simplified compared with that of a real butterfly. Fig. 7 shows the constructedhardware.

3.2. Motion analysis and discussion

To clarify the relationships among flapping angle, abdomen angle and pitch angle during takeoff, wephotographed the flight motion of the constructed hardware during takeoff using the same three-dimensionalhigh-speed camera system, but with 400 fps, and analyzed the obtained images. Fig. 8 shows stroboscopicphotographs of the front view and side view taken every 5ms during takeoff. Here, the origin of coordinatesillustrates the initial position of the center of mass. Fig. 9 shows a typical example of the relationships amongthe flapping angle, the abdomen angle and the pitch angle during takeoff. As shown in this figure, wequalitatively realized the same relationship between flapping angle and abdomen angle during a single strokeof a butterfly. However, quantitative values of flapping and abdomen angles were not realized. Additionally,we could not realize the phase reversal relationship between the abdomen angle and the pitch angle. This iswhy the constructed hardware started to fall from the head, since it could not maintain the required lift duringan upstroke. It is considered that the center of mass was located further forward in the constructed hardwarethan in a butterfly. Figs. 10 and 11 display the thorax trajectory during takeoff and the acceleration trajectoryof the center of mass of the constructed hardware. As shown in these figures, the constructed hardwaregenerated the force necessary to lift its own weight during a downstroke (‘‘A’’ in Figs. 10 and 11), and could fly

Crank

z

Wing

Connecting rod

y x

Abdomen

Abdomen angle

z

Flapping angle

Slider

Stroke of flapping

Stroke of abdomen swing

Fig. 6. Mechanism of constructed hardware: (a) flapping mechanism of the wing and (b) abdomen swinging mechanism.

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Fig. 8. Stroboscopic photographs taken during takeoff of the constructed hardware: (a) front view and (b) side view.

Fig. 7. The pictures of the constructed hardware: (a) front view of the constructed hardware; (b) side view of the constructed hardware;

and (c) comparison of a butterfly (left) and the constructed hardware (right).

T. Fujikawa et al. / Mechanical Systems and Signal Processing 22 (2008) 1304–1315 1309

upward during the downstroke. In this experiment, the maximum height and z-direction acceleration were7.9mm and 3.2G, respectively.

4. Numerical analysis

4.1. Modeling of the constructed hardware

In this study, we numerically analyzed the motion of the constructed hardware and the flow fieldaround it. A butterfly achieves lift through the interaction with the effective vortex generated by wing

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Time [ms]

Ang

le [

deg]

Flapping angleAbdomen anglePitch angle

Fig. 9. An example of the relationship among flapping angle, abdomen angle, and pitch angle of the constructed hardware during takeoff.

A

X [mm]

Z [

mm

]

Fig. 10. Trajectory of the center of mass of the constructed hardware during downstroke.

T. Fujikawa et al. / Mechanical Systems and Signal Processing 22 (2008) 1304–13151310

deformation during flapping. Based on this observation, we developed a computational model for analyzingbody motion including the abdomen, the deformation of the wing, and the flow field around it. These aresolved using a weak coupling method that allows the use of different space resolution and different samplingtimes.

The body consists of three mass points, the head, thorax, and abdomen, which are connected by springs anddampers. The shape of the wing is defined as a single convex rectangle because the fore- and hind-wings movesynchronously. The wing is divided into rectangular segments, Nx�1 of them along the x-axis and Ny�1along the y-axis. A mass proportional to the area of the segment is assigned to each segment. Mass points onthe wing are also connected by a spring and a damper to each other, with the spring constant representing therigidity of the vein. Like the mass points on the wing, the thorax of the body and the vertices of the wings arealso connected by springs and dampers. Fig. 12 shows the robot model used for numerical simulation.Note that two actuators are employed, one for flapping (A1 in Fig. 12) and one for abdomen swing (A2).They move synchronously as described in Section 3.1. The wings are made symmetrical for simplicity inthis study.

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A

z” [

G]

x” [G]

Fig. 11. Acceleration of the center of mass of the constructed hardware during a stroke.

z

y

z

A2Actuator

xLeft wing

Head

x

yjNy-1

A1Actuator

Translational springs and dampers Rotational springs and dampers

Thorax

Abdomen

i

Nx-1

Fig. 12. Models for numerical simulation: (a) side view; (b) top view; and (c) back view.

T. Fujikawa et al. / Mechanical Systems and Signal Processing 22 (2008) 1304–1315 1311

The equation of motion of each mass point is given by

mi;j €xi;j ¼ f Xi;j þ TX

i;j cos jxi;j cos y

xi;j � TX

i�1;j cos jxi�1;j cos y

xi�1;j þ TY

i;j cos jy0;j cos y

y0;j � TY

i;j�1

� cos jy0;j�1 cos y

y0;j�1

mi;j €yi;j ¼ f Yi;j þ TX

i;j cos jxi;j sin yx

i;j � TXi�1;j cos j

xi�1;j sin yx

i�1;j þ TYi;j cos j

y0;j sin yy

0;j � TYi;j�1

� cos jy0;j�1 sin yy

0;j�1

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mi;j €zi;j ¼ f Zi;j þ TX

i;j sin jxi;j � TX

i�1;j sin jxi�1;j þ TY

i;j sin jy0;j � TY

i;j�1 sin jy0;j�1

TYi;j ¼ 0 ðia0Þ (1)

where i is an integer in the range from 0 to Nx�1 and j is an integer in the range from 0 to Ny�1, as shown inFig. 12, yx

i;j is the angle from the x– z plane and yyi;j is the angle from the y– z plane of the mass point (i, j), fx

i;j

and fyi;j are the angles from the x– y plane on the left side of Fig. 13, Rx

i;j and Ryi;j are the link lengths in the

directions of the x and y axes, mi,j is the mass, f is the net force of the two actuators, the flow field, the gravity,the spring, and the damper, and T is the tension. The difference between the upper and lower pressures of theflow field is added to the mass point as a force proportional to the area, as shown on the right side of Fig. 13.Using these equations, the global equation, ½M�½ €X � ¼ ½F �, is formulated and then the body motion and wingdeformation are solved by a fourth-order Runge Kutta method. Here, [M] is a global mass matrix, ½ €X � is aglobal acceleration vector, and [F] is a global force vector.

The flow field around the wing is solved using the following Navier–Stokes equations and the equation ofcontinuity based on three-dimensional, incompressible, viscous and unsteady flow:

qv

qtþ n � rn ¼ �

1

rrPþ

mrr2n (2)

r � n ¼ 0 (3)

Here, v is the velocity, P is the pressure, r is the density of air and m is the viscosity. To treat the largedeformation of the wing over time, we used FEM, which offers both geometric flexibility, by allowing the useof unstructured grids, and high spatial accuracy, by using a hexahedron with eight nodes as an element. Thearbitrary Lagrangian–Eulerian (ALE) method was used for the movement of the boundary of the wing. Thesimplified marker and cell (SMAC) method, which separates pressure and velocity, was adopted for fastcomputation. The streamline upwind Pedrov–Galerkin (SUPG) method was employed to stabilize thecomputation. In addition, the Galerkin method of using the shape function as a weight function wasemployed. Meshing in the computational space was performed at each sampling time. In this method, eachnode is connected by virtual springs and moves according to kinematics during wing deformation.

Our proposed computational scheme consists of the following main processes: (a) motion and structurecomputation by the Runge Kutta method, (b1) mesh generation for the flow field, (b2) matrix creation, and(b3) inverse matrix calculation. By this method, the computation is performed as follows: (step 1) the bodymotion and the wing deformations are calculated while the flow field is fixed; (step 2) the flow field iscalculated while the boundary conditions on the body and wing are fixed. Steps 1 and 2 are then iterated by theweak coupling method. Thus, the position and velocity of each mass point calculated in step 1 are used asboundary conditions in step 2 and the pressure on the wing calculated in step 2 is converted into the force onthe wing in the next step 1 (see Ref. [20] for details).

Motion analysis during takeoff was performed using the structural parameters corresponding to those ofthe constructed hardware. Spring and damper constants were determined by pilot experiments and those ofthe leading edge (i ¼ 0) were set to be 10 times larger, to express the high rigidity of the bamboo frame. Theparameters for the computational scheme were as follows: wing divided into Nx ¼ 10 and Ny ¼ 16, actuatortorques proportional to the flapping angle, sampling times for the computation of the body motion/wing

yz

x

jX ,0

jx

,0θj

xR ,0

jyR ,0

jx

,0ϕj

x,0θ

jx

,0ϕ10 +,jX

,jX 1

,jX 2

11 +,jX

i, j

1PΔ2PΔ3PΔ

4dS

2dS1dS

4PΔ3dS

Fig. 13. (a) Definition of mass points and (b) assigned pressure on wing.

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deformation and of the flow field of 0.01 and 0.1ms, respectively, and FEM node number of about 500,000.The computational space for the left side of the manufactured hardware was set to be 770mm�393mm� 660mm, which is almost six times the wing length in both upstream and downstream directions.

4.2. Results and discussion

Fig. 14 shows stroboscopic images of the pressure contours in the plane including leading edges during adownstroke corresponding to Fig. 8(a). As shown in Fig. 14, we found that the negative vortices created at thetip of the leading edge grow and spread over the whole of the wing. Additionally, the forewings bended up likea camber and the hind-wings rolled up. This result shows that a butterfly with elastic membrane wingsgenerates effective separation vortices using such mechanical properties and gets large lift. Note that althoughan airplane with fixed and high aspect ratio wings generates steady and 2D vortices, a butterfly with elastic andlow aspect ratio wings generates unsteady and 3D vortices.

The process requiring the most calculation cost was the mesh generation, particularly when the wingdeformation or flapping angle was large. The computational scheme could stably generate a mesh up to 801 ofthe flapping angle, for which the maximum distortion angle of the element was less than 401. It was difficult togenerate a mesh with little distortion in the neighborhood of the flapping angle of 901, as the right and left

Fig. 14. Pressure contours in the plane including leading edge during downstroke.

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wings overlapped. However, since most butterflies acquire great lift by flying under this condition, meshcontrol at this critical angle is important.

5. Conclusions

In order to develop a small flapping robot, we investigated the flight mechanism of a butterfly using a three-dimensional high-speed camera system. We also constructed an isometric hardware model based on thestructure and mechanism determined from the analysis of butterfly flight and compared the motions of thebody and wing with that of a butterfly. We then proposed a new computational scheme of FEM, for solvingthe body motion, including abdomen swing, wing deformation and flow field around the wing, and analyzedthe vortex around the wing of the constructed hardware during takeoff.

By investigating the flight motion of a butterfly during takeoff, we showed that a butterfly flies upward bymoving its abdomen up during the downstroke and flies forward by moving its abdomen down during theupstroke. Also, the flapping and abdomen angles changed at the same frequency but were in antiphase.

The constructed hardware realized the same relationship between flapping and abdomen angles during boththe upstroke and the downstroke as that of a butterfly. In addition, it generated the force necessary to lift itsown weight during a downstroke. However, the quantitative values of the angles of the constructed hardwareand a butterfly did not correspond to each other, since hardware constraints did not allow the center of massof the constructed hardware to match that of the butterfly. The relationship between the abdomen angle andthe pitch angle was not fully realized.

By numerical simulation, we showed that the negative vortices created at the tip of the leading edge growand spread over the whole wing. These unsteady and 3D vortices were the main factor in generating lift.

In future work, we aim to realize butterfly-like takeoff by establishing the control method of the pitch angleand constructing hardware that can generate the force necessary to lift its own weight during the upstroke aswell as the downstroke. Additionally, we aim to visualize the flow around the wing of the constructedhardware. Furthermore, we intend to investigate the reliability of calculations and to stably control meshgeneration for numerical computation in the neighborhood of a flapping angle of 901.

Acknowledgments

This research was supported by the Japan Society for the Promotion of Science (JSPS), Grant-in-Aidfor Young Scientist (A), 17686022, 2005. The authors would like to express their deep gratitude to allthose involved in the research project, particularly, Prof. M. Yamamoto of Tokyo University of Science andProf. K. Toda of Chiba Institute of Science for advice on fluid analysis.

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