High-Speed, Three-Dimensional Quantification of Ladybug (Hippodamia convergens) Flapping Wing Kinematics During Takeoff

Transcription

1 High-Speed, hree-dimensional Qantification of adbg (Hippodamia conergens) lapping Wing Kinematics Dring akeoff an B. George, Scott. homson Department of Mechanical Engineering, Brigham Yong Uniersit, Proo, U, 846 adbg wing and bod kinematics dring takeoff is eplored g high-speed stereoscopic images acqired at a rate of 3 frames per second. A direct linear transformation algorithm is sed to qantif positions of selected locations on the bod, forewings (eltra), and hindwings. Design and setp of instrmentation and analsis procedres are eplained. lapping freqenc is reported. Significant motion of the forewing and other findings are presented and their applications are discssed. omenclatre [ ] Coordinates in Cartesian space (cm),, position of object in left iew frame (piels),, position of object in right iew frame (piels) eft image calibration ector ight image calibration ector H Homogeneos transformation I. Introdction he se of flapping flight is biqitos among the animal and insect kingdom. lapping flight, which featres an aerodnamic flight regime characteried b a relatiel low enolds nmber, ields lift-generating mechanisms. It introdces seeral adantages sch as increased agilit and abilit to naigate in confined spaces (sch as indoors). It also offers the potential for decreased detectabilit, de to redced sie and possible redced noise, and the abilit to hoer. Man aspects of flapping flight kinematics, both in natral and man-made sstems, howeer, are et to be fll nderstood. Sch aspects inclde phenomena de to deformable and/or adjstable wings and wing kinematics, and the wide ariabilit in wing sie, wing shape, and wing and bod kinematics. One particlar aspect of interest is the inflence of the forewings fond in beetles (Coleoptera). ling beetles sch as ladbgs (Hippodamia conergens) hae two stiff, protectie forewings and two flapping hindwings. he forewings, known as eltra (or eltron, glar), coer the hindwings when not in flight, bt moe pward and forward dring flight. he also perform other fnctions sch as trapping moistre, protection, etc. he role of the forewing dring flight, howeer, has not been thoroghl eplored; nor hae the wing kinematics and aerodnamics of the forewing-hindwing combination. he goal of the present research is to anale beetle flapping wing kinematics g ladbgs as sbjects. A series of high-speed images of a ladbg dring takeoff to qantif the three-dimensional position of points on the bod, forewings, and hindwings has been analed to qantif forewing opening, hindwing motion dring flapping, and bod motion dring takeoff. esearch Assistant, Mechanical Engineering, 435 CB, AIAA Stdent Member. Assistant Professor, Mechanical Engineering, 435 CB, AIAA Member. American Institte of Aeronatics and Astronatics

2 II. Methods A. Oeriew he approach of the present research is to anale flapping wing kinematics g high-speed stereoscopic imaging. A direct linear transformation (D) is applied in order to correlate the two-dimensional stereoscopic image coordinates into three-dimensional Cartesian spatial coordinates. he goal is to conert this data into appropriate kinematic representations for se in inestigating the role of the forewing in flapping flight and to std deformable wing shape kinematics of ladbgs. B. Data Acqisition As illstrated in ig., the eperimental setp inoles a Photron APX-S high-speed digital camera, a mirror arrangement for projecting two iews of an object onto a gle camera image, and a combination of ED and incandescent lighting. he frame rate of the camera is set to 3 frames per second while the shtter speed is /6 th of a second. his higher shtter speed ensres a relatiel complete freee of the wing motion. A ikon 5mm ikkor lens is sed with an apertre of. Prior to image acqisition, a calibration target was created g /6 th inch diameter etrded wire soldered together to form a grid pattern. he target consists of 5 tiers with 5 white dots painted on each tier, proiding a total of 5 calibration points. he target was placed in the camera s field of iew, so that two iews of the target are isible in the camera image (see ig. ). wo iews of test object isible in image Otpt Incandescent light Highspeed camera Incandescent light Mirrors ED ED est object ED ED igre. High-speed imaging setp. American Institte of Aeronatics and Astronatics

3 American Institte of Aeronatics and Astronatics 3 igre. Calibration target as iewed g setp shown in ig.. C. Data Analsis Matlab is the primar tool sed to anale the high-speed images. A Direct inear ransformation (D) implementation, cstom coded in Matlab, is sed. he D is here briefl described; frther details can be fond elsewhere 3,4. D is a method of determining the three dimensional location of an object (or points on an object) in space g two different iews of the object. here are a ariet of was of attaining mltiple images; howeer, the approach sed here is one camera and an arrangement of mirrors. his allows for the relatie distances between the camera, mirrors, and object to be aried oer a sfficientl wide range. his method is also beneficial ce it reqires onl a gle camera and reqires no temporal snchroniation between sets of images. Calibration is fond g isible calibration points on the aforementioned calibration target. Calibration consists of finding ectors and g the following series of eqations. irst, M M , () is calclated, where is the nmber of calibration points, i, i, and i (i to ) are the known positions of the calibration points, i and i are the horiontal and ertical piel locations, respectiel, of the points in the images, and throgh are the calibration constants. Similarl, ( throgh ) is fond b replacing i, i, and with i, i, and. If we denote the first matri on the left-hand side as and the right-hand side matri as g, then g the Moore-Penrose psedo-inerse method, we can write ( ) g, ()

4 American Institte of Aeronatics and Astronatics 4 and similarl for ( ) g. (3) he position of an point isible from two perspecties in the image can then be fond g the eqation (4) Denoting the first matri on the left-hand side as Q and the right-hand side matri as q, Eq. (4) can be written as q Q, (5) from which the Moore-Penrose psedo-inerse method can be applied to find the position of the nknown Cartesian coordinates,, and : ( ) q Q Q Q. (6) In the present research, the and calibration matrices are fond g the calibration target. A ladbg is then placed in the field of iew and images of the ladbg are acqired dring takeoff. he,, and locations of for points on the ladbg are then tracked. he points inclde a point near the front of the bod, a point near the rear of the bod, and the tip of both forewings and hindwings. Once 3D Cartesian spatial coordinates hae been fond, a set of homogeneos matrices can be applied in order to anale data in a more relatie plane. his is accomplished ia se of a rotation transformation, contained in a 33 sb-matri of the homogeneos transformation (H), which we will denote b. A rotation b in the -ais, a rotation b in the -ais and a rotation b in the -ais, respectiel, can be represented b ),, ( (7) he translation transformation is represented b p, (8) where,, is the ector representing the location from the origin of the initial frame to the origin of the new relatie frame. Homogeneos matri H when matri mltiplied with the 3D Cartesian coordinate, reslts in the new resoled Cartesian coordinate ) (3 3) (3,],, [ old old old new new new p. ()

5 Each data set was rotated manall g its own homogeneos matri to allow analsis of flapping wing and bod kinematics. III. eslts Calibration of and ectors g the calibration target reslted in an aerage coordinate error of.47 cm. igre 3 shows the known positions of the points on the calibration target. etrning the piel locations of the calibration points into Eq. (6) allows for an estimate of the qalit of the calibration data. he comparison between actal and calclated points is adeqate. D analsis has been performed on 5 data sets (all different ladbgs), or,344 frames of data. In each data set, both forewings, both hindwings, the front bod, and rear bod hae been qantified. igre 4 shows two images of the ladbg; one shortl after takeoff initiation, and another a short time later. hese images show the coordinate sstem sed. igre 3. Calibration arget eslts 5 American Institte of Aeronatics and Astronatics

6 igre 4. Image seqence showing first and last frame coordinate sstem. Initiation of flight ermination of data analsis igre 5. Smbols showing three-dimensional paths of si ladbg anatomical landmarks. he dashed black lines connect the front and rear bod points, illstrating the approimate ladbg attitde, at select times. igre 5 plots a time histor of the positions of the si points on the ladbg dring takeoff. his demonstrates sccessfl implementation of image analsis of the ladbg specimen. It is interesting to note that the forewing moes in nison with the hindwing with a relatiel large amplitde. his ma be a passie refle, althogh frther inestigation is reqired to determine this. igre 6 shows an eploration of ertical displacement of both forewing and hindwing. It is apparent that a brief -direction reersal occrs in the middle of the flapping stroke ccle when the hindwing transitions shape. igre 7 shows a comparison of this phenomenon oerlaed with ideo images to isalie what is taking place. 6 American Institte of Aeronatics and Astronatics

7 igre 6. Horiontal () position of forewing and hindwing. igre 7. Visal eploration of flapping wing s. ideo images. igre 8 shows the hindwing eleation (-position) s. time. A flapping freqenc analsis shows an aerage flapping freqenc of 78.6 H (see able ). igre shows reslts from an analtical analsis of bod elocit. eslts indicate that the specimen is traeling at an aerage elocit of abot.4 cm/second. 7 American Institte of Aeronatics and Astronatics

8 4 3 igre 8. Hindwing eleation () s. time. able. reqenc of ladbg flapping. Period ime (Seconds) reqenc (H) Aerage reqenc 78.6 igre. Bod ertical displacement s. time, along with linear cres fit to estimate aerage elocit. 8 American Institte of Aeronatics and Astronatics

9 igre displas a seqence of images which help isalie the fleible natre of the hindwing. Wing rotation and deformation is eident, as has been obsered elsewhere; this allows the airfoil shape of the wing to prodce lift oer the blk of the insect s flapping period and contribtes to other lift-enhancing phenomena. igre shows a ladbg dring takeoff and transitioning into horiontal flight. It is obsered that the amplitde of the stroke eleation is large, at first, and then transitions into smaller, stead, strokes. igre shows an eploration of ertical displacement of both forewing and hindwing. igre. Image seqence showing hindwing deformation. igre. adbg wing amplitde steadil decreases as it transitions to stead flight. American Institte of Aeronatics and Astronatics

10 igre. Vertical () position of forewing and hindwing. left forewing in open position right forewing in open position forewing in closed position igre 3. 3-D qantification of ladbg forewings. igre 3 shows a qantification of both forewings of a ladbg specimen dring opening. his kinematic identification shows that these forewings do not simpl follow a straight line approach to their takeoff position, bt follow a cred path. inall, in ig. 4, a niqe behaior of the legs can be seen he nd image in the seqence show the legs moing otward and the 3 rd image in the seqence show the legs in an almost fll etended position. We hae consistentl obsered this phenomenon in ladbgs. he prpose for this behaior is crrentl nknown. American Institte of Aeronatics and Astronatics

11 legs legs legs igre 4. Image seqence showing ladbg leg etension. IV. Conclsion he work presented represents reslts from data acqired from a series of high-speed images of a ladbg dring takeoff. hese reslts illstrate the fnctionalit of the D implementation and calibration techniqe, the sccessfl data acqisition of a ladbg in takeoff and free flight, and show analsis of seeral seqences of ideo image data. Data of this tpe ma be sefl in inestigating the aerodnamics of insect flight, inclding the deelopment and analsis of comptational and eperimental models. Of particlar interest will be the aerodnamic interaction of the relatiel stiff (bt clearl not static) forewing-generated ortices with those generated b the mch larger hindwings. Acknowledgments Spport for.g. of a research award from the Brigham Yong Uniersit Office of esearch and Creatie Actiities (OCA) is gratefll acknowledged. eferences Sh, W., ian, Y., ang, J., Viier, D., and i, H. Aerodnamics of ow enolds mber lers, Cambridge Uniersit Press, Cambridge, 8, Chapters,4. rantseich, Zhendong D, Wang W, and Zhang Y. Geometr of Eltra Opening and Clog in Some Beetles, he Jornal of Eperimental Biolog, Vol. 8, 5, pp Abdel-Ae, Y. I. and Karara, H. M. Direct inear ransformation from Comparator Coordinates into Object Space Coordinates in Close-ange Photgrammetr, Proceedings of the ASP/UI Smposim on Close-ange Photogrammetr (American Societ of Photogrammetr, alls Chrch, VA), 7, pp Hartle, ichard. Zisserman, Andrew. Mltiple View Geometr in compter ision, Cambridge Uniersit Press, Cambridge, 3. American Institte of Aeronatics and Astronatics