Pose Measurement Method and Experiments for High-Speed Rolling Targets in a Wind Tunnel

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1 Sensors 014, 14, ; do: /s Artcle OPEN ACCESS sensors ISSN Pose Measurement Method and Experments for Hgh-Speed Rollng Targets n a Wnd Tunnel Zhenyuan Ja 1, Xn Ma 1, We Lu 1, *, Wenbo Lu, Xao L 1, Lng Chen 1, Zhengqu Wang and Xaochun Cu 1 Key Laboratory for Precson and Non-Tradtonal Machnng Technology of the Mnstry of Educaton, Dalan Unversty of Technology, Dalan 11604, Chna; E-Mals: Jzyxy@dlut.edu.cn (Z.J.); maxn000@mal.dlut.edu.cn (X.M.); me_lx@163.com (X.L.); @mal.dlut.edu.cn (L.C.) AVIC Aerodynamcs Research Insttute, Shenyang 11604, Chna; E-Mals: F13py@163.com (W.L.); wzqnwpu@16.com (Z.W.); cu_xaochun@163.com (X.C.) * Author to whom correspondence should be addressed; E-Mal: Lw007@dlut.edu.cn; Tel./Fax: External Edtor: Vttoro M.N. Passaro Receved: 8 September 014; n revsed form: 1 December 014 / Accepted: 5 December 014 / Publshed: 1 December 014 Abstract: Hgh-precson wnd tunnel smulaton tests play an mportant role n arcraft desgn and manufacture. In ths study, a hgh-speed pose vson measurement method s proposed for hgh-speed and rollng targets n a supersonc wnd tunnel. To obtan mages wth hgh sgnal-to-nose rato and avod mpacts on the aerodynamc shape of the rollng targets, a hgh-speed mage acquston method based on ultrathn retro-reflecton markers s presented. Snce markers are small-szed and some of them may be lost when the target s rollng, a novel markers layout wth whch markers are dstrbuted evenly on the surface s proposed based on a spatal codng method to acheve hghly accurate pose nformaton. Addtonally, a pose acquston s carred out accordng to the mentoned markers layout after removng msmatchng ponts by Case Deleton Dagnostcs. Fnally, experments on measurng the pose parameters of hgh-speed targets n the laboratory and n a supersonc wnd tunnel are conducted to verfy the feasblty and effectveness of the proposed method. Expermental results ndcate that the poston measurement precson s less than 0.16 mm, the ptchng and yaw angle precson less than 0.13 and the roll angle precson 0.71.

2 Sensors 014, Keywords: machne vson; pose measurement; hgh-speed moton; wnd tunnel 1. Introducton The pose measurement method has been wdely used n many research felds such as aerospace, robots and medcal scence. In some cases, the mproper separaton of stores carred by a hgh-speed arcraft, such as bombs, auxlary fuel tank, torpedoes and mssles, wll greatly mpact the performance of the mother plane and even threaten the safety of the plot [1,]. Smulatve store separaton experments n wnd tunnels provde valuable reference for the layout desgn and release parameters of the store. However, snce wnd tunnel models are usually small-szed and move and rotate at hgh speeds, tradtonal measurements fal to correctly measure ther pose nformaton. Vson measurement has proved ts advantages such as beng non-contact and hgh precson and the ablty for real-tme measurement. Therefore, pose measurement n wnd tunnels based on vson measurement s of great mportance [3,4]. Numerous approaches for measurng the pose parameters of targets have been studed by many scholars and research nsttutons. Watzlavck et al. presented the Optotrak TM measurement system by Canada s Northern Dgtal Inc. (Waterloo, ON, Canada). Three precsely calbrated lnear CCDs are used as dsplacement sensors [5]. The 3D coordnates of each marker can be obtaned n real tme by capturng the near-nfrared lght gven out by the actve lumnous markers. The precson and resoluton of the system can reach 0.1 mm RMS and 0.01 mm, respectvely. It has been successfully appled to the aerodynamc elastcty and angle measurement of the wnd tunnel models of both Boeng and the NASA Ames Research Center. However, ts low samplng frequency and bg volume of embedded markers cannot satsfy hgh-speed pose measurement demand of small volume objects. Rock et al. combned the Carrer-Phase Dfferental Global Postonng System (CDGPS) and a bnocular vson system to dentfy ground target mages [6]. They used color object dentfcaton technology to process mages captured by the left and rght cameras, and employed two dfferent mages to locate the target projecton. Fnally, the arcraft pose parameters can be estmated accordng to stereo trangulaton. Though ths method s smple n calculaton, the wreless sgnals n a complex envronment are susceptble to be dsturbed, so the measurement data are not stable. NASA LaRC developed a pose measurement system based on bnocular vson for the wnd tunnel model [7 10]. The model mages are captured contnuously and synchronously by two CCD cameras through the observaton wndow. The pose parameters of the wnd tunnel model can be calculated after measurng the 3D centrod coordnates of crcular markers. However, ths method has dsadvantages due to the hdden phenomenon when the model s rollng. Murray et al. employed an Optcal Trackng System based on Partcle Image Velocmetry (PIV) to obtan the ptch angle, angular velocty and related pose nformaton of a hgh-speed target [11]. Though hgh-speed measurements can be acheved, they cannot get the rollng angle utlzng ths system. Chen presented a pose measurement method for expermental model based on actve vson n a wnd tunnel [1]. Ths method transforms the drect pose measurement of the target nto an ndrect measurement of spots on the wall, whch amplfes the varaton of the nformaton. Thus, the resoluton of the measurement system can be ndrectly mproved, and the maxmum error of

3 Sensors 014, dsplacement of the cooperatng target s 0.46 mm. However, ts low precson cannot satsfy pose measurement requrements of small volume hgh-speed target and hgh-speed rollng moton. Fan et al. proposed an atttude and poston trackng system for ndoor carrers based on an ntegrated navgaton fuson of INS/UWB nformaton strategy [13]. The two subsystems (INS and UWB) are ntegrated by a feedback correcton method. Then, the data fuson of the two subsystems can be realzed by an optmal comprehenson and flterng strategy. Though the poston and atttude nformaton can be obtaned n real tme, when t comes to small targets wth hgh-speed rollng moton n a wnd tunnel, the UWB technology can hardly meet the measurng envronment demands. In summary, scholars have made dfferent knds of nvestgatons on nnovatons n pose measurement under wnd tunnel condtons, but the pose measurement speed s low and the hdden phenomenon of cooperaton markers n the rollng procedure s gnored. In ths paper, a pose measurement method for hgh-speed rollng targets n wnd tunnels s presented. The remander of ths paper s organzed as follows: Secton wll detal the vson theory and mage acquston method; Secton 3 wll descrbe the marker layout on the surface of target and the mage matchng method; Secton 4 wll present the pose nformaton acquston method from the constructed markers 3D coordnates; Secton 5 wll show the results obtaned from a set of testng scenaros. Fnally, the paper ends wth conclusons about the whole pose measurement method and the results obtaned.. Measurement Method and System for Hgh-Speed and Rollng Targets.1. Bnocular Vson Theory Vson measurement focuses on how to obtan 3D nformaton from D mage nformaton. Two types of coordnate systems (.e., mage and global coordnate systems) are nvolved n transformng the D mage coordnates obtaned from the camera nto 3D global coordnate nformaton, as shown n Fgure 1. Fgure 1. The prncple of bnocular stereo magng. P = [ Xw Yw Zw] Zl Zr Xl Ol Yl p = [ u v ] p = [ u v ] l l l r r r Xr Or Yl

4 Sensors 014, In ths study, the pnhole model s taken as the magng model. However, due to some defects occurred n the manufacture and nstallaton procedures of composte lenses, mage dstorton s unavodable, resultng n aberraton between the real and theoretcal mage ponts. Therefore, we ntroduce a non-lnear magng model consderng the mpact of aberraton. The projecton equaton of the non-lnear magng model can be gven by: X w uˆ+ δ x Y R T w Z ˆ c v δ y M + = 1 T 0 1 Z w 1 1 where ( ˆ ˆ) δx δ y stand for aberraton, whch are known already; ( X w Yw Z w) represent the 3D coordnates of one pont n the world p u v represents the real pont caused by mage dstorton; ( ) coordnates; Z c s the scale factor; M 1 represents the ntrnsc parameter of the camera; rotaton matrx R and translaton matrx T are the extrnsc parameters. Wde-angle lenses are used n our measurement system to obtan close shots wth a large feld of vew, thus the man mage dstorton n our system s barrel dstorton. To obtan a computaton method wth less complex and better stablty, the frst and second order dstorton coeffcents are employed n the aberraton model, as shown below: ( ) ( ) δ ˆ ˆ ˆ ˆ( ˆ ˆ x = ku u + v + k u u + v ) ˆ ˆ ˆ ˆ( ˆ ˆ δ y = kv u + v + k v u + v ) 1 1 where k 1, k are the frst and second coeffcent of radal dstorton. Camera calbraton s the prelmnary step for establshng an accurate relatonshp between the mage and the real world. In ths paper, Zhang s D calbraton method s mplemented to acheve a hgh precson calbraton of the bnocular vson measurement system wth a wde feld of 1 m 1 m [14]. The calbraton targets are shown n Fgure. Fgure. Calbraton targets taken n dfferent angles. (1) ()

5 Sensors 014, Measurement Method In ths paper, poston and atttude parameters of hgh-speed and rollng targets can be acheved va analyzng mage sequences of markers movng trajectory whch s captured n real tme by a bnocular vson measurement system. The measurement prncple for poston and atttude parameters of hgh-speed movng targets s depcted n Fgure 3. Frstly, ultrathn retro-reflecton markers are attached on the surface of target. Then, the left and rght CCD cameras are used to capture the mage sequences by applyng the hgh-speed mage acquston technque. Moreover, the hgh-precson matchng and recognton of the correspondng markers n the left and rght mages are facltated based on spatal encodng, and then the 3D coordnates of the markers n the world coordnate system are reconstructed. Furthermore, the axs of the slender rollng target s ftted usng Case Deleton Dagnostcs. Fnally, the pose nformaton of the target s obtaned by computng the 3D coordnates of the markers. Fgure 3. Camera-tunnel arrangement. Local vew of targets Wnd tunnel Marker Bnocular cameras and lghts Targets Observaton wndows Arcraft.3. Ultrathn Retro-Reflecton Markers for Hgh-Speed Image Acquston The hgh speed mage acquston of rollng targets n a wnd tunnel manly has the followng dffcultes: (a) Owng to the lmted sze of the observaton wndow and the hgh mage acquston speed, t s dffcult to guarantee clear mages; (b) Snce the target s mostly a small-szed cylnder-lke object of complcated shape, t s dffcult to ensure the poston accuracy of markers; (c) In order to guarantee the aerodynamc shape of the scaled model, the thckness of markers cannot exceed 30 um. However, normal markers are too thck (160 μm) to meet the requrements. To solve the aforementoned problems, an ultrathn retro-reflecton markers fabrcaton technque based on a rollng-prnted method s proposed to allow the hgh speed mage acquston of hgh-speed rollng target. Ultrathn retro-reflecton markers are made by mxng glass mcrobeads, slver powder and resn accordng to the specfc mxng rato of 16:5:9. The thckness of the resultng ultrathn retro-reflecton markers s only 0 μm, whch guarantees the aerodynamc shape of the scaled model. The dagram of the rollng-prnted method s shown n Fgure 4, where the screen plate that s desgned accordng to the marker layout s placed atop the target. The ultrathn retro-reflecton materal

6 Sensors 014, s placed on top of the screen plate. When a process performs an operaton on the devce, the screen plate keeps n pure rollng contact wth the target and moves contnuously at a certan lnear speed V along the perpheral velocty drecton. V can be computed by V = ωr, where ω and r depct the angular velocty and radus of the rollng target, respectvely. As a result, the ultrathn retro-reflecton materal n the mesh openng can be pumped or squeezed by the squeegee on the surface of the target. Fgure 5 presents the fnshed target. Fgure 4. Dagram of the rollng-prnted method and structure of the screen plate. Fgure 5. The fnshed target. Makers Targets In ths way, the thckness and the postonng accuracy of markers are ensured. Besdes, mages captured by the left and rght cameras have hgher sgnal-to-nose rato and better brghtness, and the mage acquston requrements can be satsfed under hgh shootng frequency condtons. As shown n Fgure 6, the brghtness of markers decreases whle the shutter speed ncreases. However, markers are brghter and have hgher sgnal-to-nose rato at the 5000 shootng speed.

7 Sensors 014, Fgure 6. Shootng pcture of ultrathn retro-reflecton markers n dfferent frames. 5000fps 500fps 50fps 3. Image Processng In ths paper, cooperatng markers are adopted to acheve rapd pose calculaton of rollng targets. In order to mprove the stablty and precson of the results, t s necessary to attach more markers on the surface of the target. However, due to the small magng area and lack of feature nformaton, t s hard to match and recognze these markers. Ths secton descrbes how to match and recognze markers wth nformaton loss Markers Layout of Hgh-Speed Rollng Target In order to calculate the pose parameters of the movng target quckly and accurately, the followng problems must be solved: (1) t s dffcult to acqure accurate matchng and recognton of markers wth less magng area and nconspcuous moton features; () the hgh-speed rollng target n ths paper s long and thn, makng the target surface really small. Consequently, marker dstrbuton s relatvely dense, so that the recognton and matchng of large number of markers would be very dffcult; (3) markers features (quantty, seral number, layout, etc.) are also dffcult to be ascertaned durng the measurng process owng to the rollng moton of the target. To solve those problems, a spatal encodng method s presented n ths paper. Fgure 7. Markers dstrbuted along the crcumferental drecton of the target. afb afm amb F M B Tradtonal encodng methods complete the encodng process by changng the shape of a sngle marker. Combnng wth dvdng several markers nto one group based on spatal relaton, postonal relatonshp between markers n the same group s used n the spatal encodng method proposed n ths paper to realze encodng process [15]. As a result, the problem that small markers n larger feld of vew are dffcult to encode s solved. As shown n Fgure 7, each three markers are dvded nto one group

8 Sensors 014, whch s called a spatal encodng group accordng to a lnear constrant, and then the three markers can be ascertaned through the dstance rato between them. The formula can be gven by: j afm afm afm = c, j (3) a a a mb mb mb afm a a mb fm amb = l, = n, (4) a a a a fb fb fb fb where a represents dstance between the two space encodng markers n the same group of ; f, m and d stand for head, mddle, tal part of the target, respectvely; let a fm be the dstance between two markers n the head and mddle part of the target; l s the dstance rato between can dstngush the th group from all other groups; c s the dstance rato between s the dstance rato between a fm and a fb, whch a fm and a mb ; n a mb and a fb ; n ths paper, we defned V be encodng array, then the V = l c n, and the spatal encodng of markers can encodng array of group can be wrtten as [ ] be accomplshed by makng the array elements n every encodng array unque. To mprove the precson and stablty of the measurement system, t s necessary to ncrease the number of markers n the layout to satsfy the extracton precson. Moreover, a radal crcular unform dstrbuton s adopted to solve the problem of the rollng moton of the target. To meet the requrements of mage acquston, a total of 1 spatal encodng groups are attached onto the target accurately accordng to the dstance nformaton of these three markers, as shown n Fgure 8. Fgure 8. The markers layout. Target Development Markers M 1 M M 3 M 4 M 7 M 8 M 5 M 6 M 9 M 10 M 11 M 1 F 1 B 1 F B F 3 B 3 F 4 B 4 F 5 B 5 F 6 B 6 F 7 B 7 F 8 B 8 F 9 F 10 F 11 F 1 B 1 B 11 B 10 B 9 In the process of measurng the pose of the target, at least three groups wth a total of nne markers appear n the mage smultaneously. The well-proportoned dstrbuton of markers n the head, mddle, and tal part of the target guarantees the number of markers as well as the pose estmaton precson of the target.

9 Sensors 014, Feature Extracton In the complcated wnd tunnel condtons, t s dffcult to conduct the marker feature extracton due to such factors as small-szed model wth large curvature change, large feld of vew and small magng area of markers. Therefore, the gradent weghted method s employed to extract the center of the markers wth hgh accuracy. Frstly, a convoluton operaton of the mage s conducted based on a Gaussan frst-order dfferental operator n order to obtan the gradent of each pont n the mage. The Gaussan frst-order dfferental operator can be wrtten as: Then, the gradent of mage can be gven by: x x h ( x) = e σ (5) πσ (, ) G x y F x F( x, y) h x = = F F( x, y) h y y (6) The coordnates of gradent centrod of markers pattern can be expressed as: h w h w c= G j P j G j = h j= w = h j= w (, ) (, )/ (, ) (7) where c s the coordnates of the gradent centrod of the markers; G(, j ) represents the weght of pont (, j ); w and h stand for the wdth and heght of target mage, respectvely; Pj (, ) s the mage coordnate of the pont (, j ) Feature Matchng between Two Vews Gray matchng and feature matchng are generally used for the classcal and effectve mage matchng. The gray matchng method s a mathematcal procedure based on the gray nformaton and mage technque, whle features such as color, texture, shape, spatal poston extracted from two or more mages are used n feature matchng. However, hgh-precson matchng under extreme envronment condtons cannot be acheved accordng to the gray and feature nformaton due to the fact that markers captured by ultra hgh-speed cameras have a small area and the gray smlarty between each one s bg. To solve the problem, spatal encodng markers are appled to transform the tradtonal matchng method based on features nto a problem accordng to spatal constrants between markers, as shown n Fgure 9. Frstly, spatal encodng markers n dfferent groups are solated by a collnear constrant, and then the matchng relatonshp between the left and rght mages can be obtaned through comparng V Left (obtaned n Secton 3.1) of the rght mage and V Rght of left mage. Moreover, based on the eppolar constrants, the correspondng marker matchng s verfed and the msmatched markers are removed.

10 Sensors 014, Fgure 9. Matchng between left and rght mages. V Left V Rght (a) (b) Fgure 10. Spatal model of marker recognton. V Development V 1 V V 3 V 4 V 5 V 6 V 7 V 8 V 9 V V V 1 M 1 M M 3 M 4 M 7 M 8 M 5 M 6 M 9 M 10 M 11 M 1 F 1 B 1 F B F 3 B 3 F 4 B 4 F 5 B 5 F 6 B 6 F 7 B 7 F 8 B 8 F 9 F 10 F 11 F 1 B 1 B 11 B 10 B 9

11 Sensors 014, The Recognton Method The recognton process can be descrbed as follows: (a) Reconstructed markers are grouped accordng to Secton 3.3; (b) Recognton relatonshps can be obtaned by comparng n turn each encodng array V obtaned by constructon (Secton 3.1) wth the one V ( = 1, 1) determned by markers layout, as shown n Fgure Poston and Atttude Soluton The poston and atttude parameters can be obtaned by translatng the coordnates from the local coordnate system on the slender rollng target to the world coordnate system through the translaton and rotaton matrx. Frstly, the axs of the slender rollng target s ftted by Case Deleton Dagnostcs. Then the coordnates of the centrod can be solved based on the dstance and axs constrant. Moreover, the absolute poston method s appled to calculate the ntal translaton and rotaton coordnate system whch are used for the transformaton, and at last the poston and atttude nformaton can be obtaned Axs Fttng Based on Case Deleton Dagnostcs Errors caused by msmatchng ponts have a great nfluence on the axs fttng soluton. Thus, to guarantee the fttng precson, an axs fttng method based on Case Deleton Dagnostcs s proposed to remove msmatched ponts. Case Deleton Dagnostc s commonly used to assess the nfluence of observatons on the parameter estmators through subset deleton [16]. Utlzng the Case Deleton Dagnostc, the outler or strong nfluence ponts are dagnosed by comparng the statstc dfference between the deleted model and un-deleted model, thus the gross errors can be removed. Specfcally, suppose that the data s P = { P1, P,, Pn }, when removng the th data pont, f there s a dfference between the deleted model and the un-deleted model, the outler or strong nfluence ponts can be obtaned, otherwse we can acqure the correct ponts whch have lttle mpact on statstcal results. Let the total number of the markers be n and at least nne markers can be collected accordng to markers layout. Then the pont set under the world coordnate system can be gven by: { } P P P P (,, ),( 1,,, ) where ( x, y, z) descrbe the 3D coordnates of pont a pont set. Case Deleton Dagnostc M ( ) = 1,,, n (8) P = x y z = n (9) w p n the world coordnate system. P stands for θ for axs fttng can be set up as follows: (1) The pont set s appled to ft the axs equaton L accordng to the theoretcal radus r whch represents the dstance between markers and axs. () The parameter estmators θ can be expressed as: n = 1 where d( p ) s the eucldean dstance from pont can be obtaned after deletng the pont p w. ( d( p ) ) r θ = (10) p to axs L ; axs L for slender rollng target

12 Sensors 014, (3) The estmated value θ of parameter estmators can be gven by: θ n = d( p ) r (11) = 1, w The judgment that whether the pont p w s outler or strong nfluence pont can be expressed as: θ θ ε (1) where ε represents the threshold defned above. When the above nequalty s satsfed, we can get the result that pont p w s a normal pont, otherwse t s a strong nfluence pont. The ntal pont set for Case Deleton Dagnostc M w ( θ ) s all the markers collected. Every pont s judged one by one, and a pont wthn the set can be removed f t s outler or strong nfluence pont. Afterwards, the axs can be solved stably usng the LM optmzng algorthm: n mn ( d( p ) r) = 1 x x0 y y0 z z0 st.. = = m n p y y z z z z z x x x y y + + n p p m m n d( p ) = m + n + p where P0( x0, y0, z 0) stands for one pont on the ftted axs; (,, ) d( p ) represents the dstance between pont (,, ) (13) Lmnp s the drecton vector of axs; P x y z and the ftted axs. 4.. Soluton for Centrod Poston Based on Dstance Constrant The centrod coordnates can be solved based on the dstance constrant between markers. In ths paper, about nne to twelve markers can be extracted accordng to the layout desgn. In order to mprove the centrod coordnates precson, optmzaton based on the dstance between all markers captured and centrod are carred out. However, the aforementoned dstance s dfferent, and the extracted markers have dfferent degrees of brghtness and crcularty. These factors have a dfferent mpact on the precson of the centrod coordnates. Thus, mult-ponts optmzaton based on settng weght for every pont s presented. Snce the centrod s on the axs, the centrod poston can be optmzed accordng to axs poston calculated va Secton 4.1. The optmzaton formula can be gven by: n mn ρ( Dc dc) = 1 x x y y z z st.. = = m n p c 0 c 0 c 0 (14) where ρ represents the weght value of each captured marker; Dc stands for the measured dstance between the centrod and the optmzed markers; dc s the real dstance between the centrod and

13 Sensors 014, optmzed markers; C( x, y, z ) s the centrod coordnate; (,, ) of the axs Absolute Pose Soluton c c c Lmnp stands for the drecton vector In ths paper, a pose acquston method s carred out accordng to the aforementoned marker layout. Two coordnate systems the ntal reference coordnate system (IRCS) and the local coordnate system (LRCS), are establshed to acqure the pose nformaton of the target through coordnate transformaton. The IRCS represents the reference coordnate system set up at the frst frame, whle the LRCS means the local coordnate system set up at the frame of the measurng poston. As shown n Fgure 11, when the axs fttng s fnshed (Secton 4.1) and the centrod poston determned (Secton 4.), the centrod of target P 1 s set as the orgn of the reference coordnate system and the axs of the target s defned as the Y axs of the reference coordnate system. Fgure 11. Schematc of the prncpal of absolute pose soluton. Z IRCS P1 (Centrod) Y X P X P Y [ R, T ] P1 (Centrod) Z LRCS Moreover, snce the X axs can be defned by any marker captured by cameras wth hgh mage qualty, the optmum marker P s chosen as the defnton pont. As a result, the space lne through the centrod of the target parallel to the lne through P and perpendcular to the rotaton axs of the target s defned as the X axs. Then, accordng to the rght-handed coordnate system, the reference coordnate system can be set up. To obtan the pose parameters, t s necessary to establsh local coordnate system usng the same marker P. However, marker P may not be captured at the poston measurng frame owng to the hdden markers phenomenon caused by the rollng movement. In order to establsh the local coordnate system, the three-dmensonal coordnates of all vsble makers at the frame of the measurng poston are reconstructed. Then, based on the recognton of vsble markers and markers layout, the three-dmensonal coordnates of the center of marker P can be acqured. Afterwards, the local coordnate system can be obtaned usng the same establshment prncple for the reference coordnate system.

14 Sensors 014, The relatonshp between the pont p = ( x y z) T n IRCS and the correspondng ( ) T p = x y z n LRCS can be wrtten by: x ' x x0 y ' = R y y pt 0 z' z z 0 where ( x0 y0 z 0) s the coordnates of the orgn of the target n IRCS. Moreover: x x' R y + T = y' z z' (15) (16) where: R= R R R θy θx θz cos( θy)cos( θz) sn( θy)sn( θx)sn( θz) cos( θy)sn( θz) + sn( θy)sn( θx)cos( θz) sn( θy)cos( θx) = cos( θx)sn( θz) cos( θx)cos( θz) sn( θx) sn( θy)cos( θz) + cos( θy)sn( θx)sn( θz) sn( θy)sn( θz) cos( θy)sn( θx) cos( θz) cos( θy)cos( θx) (17) As a result, the centrod poston of the target n the world coordnate system can be represented by T = pb ( x0 y0 z 0) ; θz, θ X, θy represent the three atttude parameters of the target n the world coordnate system: the yaw, ptch and roll. Accordng to the coordnates of the chosen ponts mentoned above, the poston and atttude parameters of the target can be computed. 5. Expermental Analyss Experments on pose measurement of the target n a wnd tunnel are conducted n ths paper, as well as the precson verfcaton test. In ths secton, the measurement precson of the three drectons and three angles s verfed Vson Measurement System A wnd tunnel s a dark narrow enclosure whch can only be montored by an observaton wndow wth a fxed shape. Accordng to the actual wnd tunnel structures, an ultra hgh-speed bnocular vson measurement system s set up, as shown n Fgure 1. The bnocular vson measurement system contans two hgh-speed cameras (FASTCAM SA-X), two wde-angle lenses (Nkon 1735), two low angle lghts, a shockproof platform, two electronc control platforms and a processng termnal. To mnmze the nfluence of vbratons caused by the wnd tunnel at runtme, the two cameras are placed symmetrcally on a customzed ar flotaton shockproof table. The camera system s nstalled on the electrc control platform so that t can be translated and rotated as desgned. The low angle DC lghts are nstalled on the edge of the lenses to ensure the lght requrements of mages are met.

15 Sensors 014, Fgure 1. Mechancal support and hardware for cameras. Hgh-speed cameras Lghts Vbraton solated table Electrcal control platform 5.. Measurement Experment for Rotary Target n Wnd Tunnel As shown n Fgure 13, the expermental facltes consst of a pose measurement system based on bnocular vson, an ejecton mechansm and a controllng system. Fgure 13. Layout of expermental facltes. Computer Ejecton mechansm Controllng system Measurement system In the test wth measurement feld of 1 m 1 m and measurement rate of 5000 fps, the ejecton mechansm and controllng system are utlzed to eject the target out of the tank wth a partcular velocty, angular velocty and angle. The vson measurement system s trggered to measure the pose nformaton of the target synchronously. Based on the aforementoned method, the pose measurement resulte of the rollng target are verfed.

16 Sensors 014, To calculate the actual pose parameters of the target, experments were conducted n a closed supersonc wnd tunnel (FL-3). The faclty layout for the wnd tunnel tests s shown n Fgure 14. Fgure 14. Faclty layout for the wnd tunnel test. Target Arcraft model Test secton of wnd tunnel Measurement system Specfcally, an arcraft model s nstalled n the nner wall of the test secton, and the ejecton mechansm s nstalled n the ejecton cabn of the arcraft model. Besdes, the measurement system s arranged outsde of the test secton to measure the pose parameters of the object n real tme through the observaton wndow. Fgure 15. The results of the poston measurement n the wnd tunnel X Dsplacement (mm) Y Dsplacement (mm) Z Dsplacement (mm) Dsplacement (mm) Tme (s) Quck pose measurements of the hgh-speed and rollng target wth dfferent nerta parameters under dfferent Mach wnd speeds are conducted. For nstance, tests under 0. Ma, 0.4 Ma and 1.5 Ma, are completed n the transonc wnd tunnel. Afterwards, the pose parameters can be gven n the wnd tunnel coordnate system, n whch the X-axs and Y-axs are parallel to the arflow drecton and the drecton of gravty, respectvely. Addtonally, one pont on the arplane cabn door s selected as the orgn of the

17 Sensors 014, wnd tunnel coordnate system and the Z-axs s establshed accordng to the rght-handed system. The measured results for certan types of targets wth 1.5 Mach speed are depcted n the followng dagrams. The results of the poston measurement are shown n Fgure 15, and the results of the atttude measurement are shown n Fgure 16. Fgure 16. The results of the atttude measurement n wnd tunnel Ptch Angle ( 0 ) Yaw Angle ( 0 ) Roll Angle ( 0 ) Angle ( o ) Tme (s) Expermental results ndcate that the quck ntellectualzed pose measurement of the target can be guaranteed by the proposed method and establshed measurement system. Accordng to the expermental analyss, three man factors affect the pose measurement accuracy: (a) Problems such as large measurng range, lmtaton of the resoluton of the ultra-hgh speed camera drectly affect pose measurement precson of the target; (b) The extracton accuracy of the markers s affected due to factors such as small volume, surface profle of markers and random deformaton durng the rollng process Precson Verfcaton Test n Laboratory In ths paper, targets are fxed on a hgh precson moton control stage. The X, Y, Z axs poston measurement precson s verfed through shootng the movement of targets when the moton control stage moves a fxed dstance along the X, Y, Z axs drecton wth hgh precson. Then the atttude measurement precson of the measurement system s verfed wth the target rotatng around the X, Y, Z axs wth a fxed angle. The expermental facltes are shown as Fgure 17. For each camera, a hgh precson moton control stage combnng a dsplacement platform and a rotary platform s bult. Wth a poston precson of mm, the moton control stage s used to mplement the specfed movng dstance of targets. Twenty four dsplacement accuracy verfcaton test runs were conducted, and the target moved 0 mm n each run. Twenty four angle accuracy verfcaton test runs were also conducted, where the target rotated fve degrees around the three axes, respectvely, n each run. The dsplacement measurement precson n each run s depcted n Fgure 18. The measured angle precson n each run s shown Fgure 19.

18 Sensors 014, As shown n Fgures 18 and 19, the mean square error of the dsplacement measurement n the X drecton s 0.13 mm, whle n the Y drecton t s 0.14 mm, and n the Z drecton 0.16 mm. The man errors manly come from errors n the markers center extracton and camera calbraton. The mean square error of the ptchng angle precson s 0.115, and that of the yaw angle precson The hgh-precson soluton of the measurement system for ptchng angle and yaw angle results from the hgh-precson of axs fttng. The roll angle precson s 0.71, manly due to the small dameter of the object to be tested. In concluson, the expermental results ndcate that the proposed method can exhbt hgh accuracy for the poston and atttude measurement of hgh-speed and rollng targets n a wnd tunnel. Fgure 17. The calbraton dagram of measurement system. Fgure 18. The poston measurement precson. Dsplacement Devaton(mm) X Devaton (mm) Y Devaton (mm) Z Devaton (mm) Translaton (mm)

19 Sensors 014, Fgure 19. The angle measurement precson Ptch Angle ( o ) Yaw Angle ( o ) Roll Angle ( o ) Angle Devaton( 0 ) Angle( 0 ) 6. Conclusons In ths paper, we have presented a pose measurement method for wnd tunnel tests to measure hgh-speed and rollng targets. A hgh-speed mage sequence acquston method based on ultrathn retro-reflecton markers s presented to ensure hgh brghtness and SNR. Ultrathn retro-reflecton markers attached on the surface of a target by a rollng-prnted method s as thn as 0 μm, guaranteeng the aerodynamc shape of the scaled model. A novel marker layout on the bass of spatal codng s proposed to ensure that markers are dstrbuted evenly on the target surface and to acheve hgh-accuracy pose nformaton. Ths layout overcomes the problem of the nformaton loss of markers when the target s rollng and ensures matchng, so that accurate marker recognton can be obtaned. Moreover, a pose parameter computng method s proposed accordng to the markers 3D coordnates. Besdes, an axs fttng method based on Case Deleton Dagnostc can ncrease the stablty of the measurement system and reduce the errors caused by msmatchng. The expermental results descrbed above ndcate that the proposed pose measurement system and method can acheve hgh accuracy and stablty, and meets the requrements of wnd tunnel tests. Fnally, the rapd pose measurement wth hgh precson for rollng targets s accomplshed n a transonc wnd tunnel envronment, and good results are acheved. Our future research wll focus on mprovng the pose measurement precson by algorthm optmzaton. Acknowledgments Ths paper s supported by the Natonal Natural Scence Foundaton of Chna (Grant No ), and the Scentfc Research Fund of Laonng Provncal Educaton Department (Grant No. L013035), and the Scence Fund for Creatve Research Groups of Chna (Grant No ).

20 Sensors 014, Author Contrbutons Zhenyuan Ja and We Lu developed the pose measurement method; Xn Ma proposed the ultrathn retro-reflecton marker fabrcaton technque; We Lu was responsble for the recognton and matchng of mages; Xao L and Lng Chen partcpated n the desgn of the expermental facltes for the wnd tunnel; Wenbo Lu, Zhengqu Wang and Xaochun Cu carred out the wnd tunnel tests and the most of the analyses. All authors wrote the paper together. Conflcts of Interest The authors declare no conflct of nterest. References 1. Lee, J.J.; Ho, H.N.; Lee, J.H. A Vson-based dynamc rotatonal angle measurement system for large cvl structures. Sensors 01, 1, Marrón-Romera, M.; García, J.C.; Sotelo, M.A.; Pzarro, D.; Mazo, M.; Cañas, J.M.; Losada, C.; Marcos, Á. Stereo vson trackng of multple objects n complex ndoor envronments. Sensors 010, 10, Newman, B.; Yu, S. Development of a Hgh Accuracy Angular Measurement System for Langley Research Center Hypersonc Wnd Tunnel Facltes. Langley Research Center: Hampton, VA, USA, August Park, H.S.; Km, J.Y.; Km, J.G.; Cho, S.W.; Km, Y. A new poston measurement system usng a moton-capture camera for wnd tunnel tests. Sensors 013, 13, Watzlavck, R.L.; Crowder, J.P.; Wrght, F.L. Comparson of model atttude systems Actve target photogrammetry, precson accelerometer, and laser nterferometer. In Proceedngs of 19th Advanced Measurement and Ground Testng Conference, New Orleans, LA, USA, 17 0 June 1996; do:10.514/ Rock, S.M.; Frew, E.W.; Jones, H.; LeMaster, E.A.; Woodley, B.R. Combned CDGPS and vson-based control of a small autonomous helcopter. In Proceedngs of the Amercan Control Conference, Phladelpha, PA, USA, 1 6 June 1998; pp Jones, T.; Lunsford, C. Desgn and development of a real-tme model atttude measurement system for hypersonc facltes. In Proceedngs of 43rd AIAA Aerospace Scences Meetng and Exhbt, Reno, NV, USA, January 005; do:10.514/ Crawford, B.L.; Rhode, M.N. Mnature on-board angle of attack measurement system for hypersonc facltes. In Proceedngs of 5th AIAA Aerodynamc Measurement Technology and Ground Testng Conference, San Francsco, CA, USA, 5 8 June 006; do:10.514/ Burner, A.W.; Flemng, G.A.; Hoppe, J.C. Comparson of three optcal methods for measurng mode deformaton. In Proceedngs of 38th Aerospace Scences Meetng & Exhbt, Reno, NV, USA, January 000; do:10.514/ Graves, S.S.; Burner, A.W. Development of an ntellgent vdeogrammetrc wnd tunnel measurement system. In Processng of Optcal Dagnostcs for Fluds, Solds, and Combuston, San Dego, CA, USA, 9 July 001; do: /

21 Sensors 014, Murray, E.N.; Jansen, J.B.; Gu, L.C.; Sener, M.J.; Brkbeck, R. Measurements of store separaton dynamcs. In Proceedngs of 47th AIAA Aerospace Scences Meetng ncludng The New Horzons Forum and Aerospace Exposton, Orlando, FL, USA, 5 8 January 009; do:10.514/ Chen, J.C.; Guo, M.; Dng, Z.L.; Yuan, F. Stereo vson based atttude measurement of arcraft model n wnd tunnel. J. Appl. Opt. 010, 31, Fan, Q.; Wu, Y.; Hu, J. Integrated navgaton fuson strategy of INS/UWB for ndoor carrer atttude angle and poston synchronous trackng. Sc. World J. 014, 13, Zhang, Z.Y. Camera calbraton wth one-dmensonal objects. IEEE Trans. Pattern Anal. Mach. Intell. 004, 6, Brown, L.G. A survey of mage regstraton technques. ACM Comput. Surv. 199, 4, Chrstensen, R.; Pearson, L.M.; Johnson, W. Case Deleton Dagnostcs for mxed models. Technometrcs 199, 34, by the authors; lcensee MDPI, Basel, Swtzerland. Ths artcle s an open access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton lcense (