Constructing Gyro-free Inertial Measurement Unit from Dual Accelerometers for Gesture Detection

Transcription

1 Sensors & ransduers Vo. 7 Issue 5 May 04 pp Sensors & ransduers 04 by IFSA Pubishing S. L. Construting Gyro-free Inertia Measurement Unit from Dua Aeerometers for Gesture Detetion Xianguo WANG Chunei YANG Dept. of Information ehnoogy Luoyang Norma University 7 Longmen oad Luoyang 470 China Dept. of Information Engineering Henan University of Siene and ehnoogy 63 Kaiyuan oad Luoyang 4703 China e.: (+86) E-mai: kevinx.water@gmai.om eeived: 8 Apri 04 /Aepted: 7 May 04 /Pubished: 3 May 04 Abstrat: Inertia measurement unit for gesture-based interfae is haraterized by short samping time and ower umuative errors whih indiates that MEMS sensors are suitabe for gesture motion detetion. his paper presents a onfiguration sheme of gyro-free miro inertia measurement unit based on dua MEMS aeerometers and orresponding methods for auating anguar rates and inear aeerations. he unit is onstruted from two triaxia MEMS aeerometers with the near-symmetria ayout; two-vaue soution spae of anguar rates an be obtained by differentia method by introduing an energy funtion the optimum estimation of anguar rates an be ahieved by soving a onvex optimization probem reated to funtion regression; for raising auray Kaman fitering method is used for denoising arguments by defining proper state & observation equations. he unit is sma and omparativey easy to hod for its near-symmetria struture aong major axis; orresponding agorithm is free from umuative errors and easy for impementation. he simuation resuts show that the sheme and reated agorithms are feasibe and effetive. Copyright 04 IFSA Pubishing S. L. Keywords: Gesture detetion Inertia measurement Gyro-free MEMS aeerometer Funtion regression Kaman fitering.. Introdution Differing from existing two-dimensiona interation methods and devies [] suh as keyboards eetroni writing pads touh sreens and so on gesture-based interation tehnoogies an fufi input tasks we by severa steps: samping anguar rates and inear aeeration of the hand-hed unit auating gesture traes and pattern reognition [ 3]. As it is physia and tangibe orresponding researhes are beoming muh more ative. One of the key steps in gesture interation is auating the ground aeerations (reative to gravity) aording to gyrosope and aeerometer outputs (reative to the unit itsef) and this task an be fufied based on inertia navigation tehnoogy. oday famiiar shemes of inertia measurement unit inude ) the ombinationa one whih onsists of both aeerometer and gyro [4] and ) the simpified one omposed of singe aeerometer [5]. Beause MENS gyrosopes have arger random drift errors and poor shok resistane abiity and an not meet the arge anguar rate measuring requirements 34

2 Sensors & ransduers Vo. 7 Issue 5 May 04 pp so the first sheme is not aways reiabe. Meanwhie the seond one has drawbaks suh as: gesture regions are strity imited and the gesture motions are not very fexibe. Sine DiNapoi and Shuer presented gyro-free methods for anguar rates measurement in 965 [6 7] theories and tehniques of gyro-free inertia navigation have been studied widey. eenty a ot of researhes about navigation systems gesture and human motion patterns reognition are arried out. Among them six and nine aeerometers onfigurations as desribed in papers of S. J. Merhav Afred. Shuer Lee Souhen and Liu Cheng-Yu [8 9] are most representative. But onsidering the imited size of measurement units these shemes are not suitabe for gesture-based interations yet beause of the ompiated spatia ayout of aeerometers [0]. Meanwhie there is a simpified sheme haraterized by threeaeerometers and estimating anguar rates through interpoation auation [ ]. From ak of vaid earning sampes it shoud be unfeasibe when gesture varies argey. In his paper we fous onstruting the gyro-free inertia measurement unit from two triaxia MEMS aeerometers and how to get the primitive features of gestures suh as anguar rates and inear aeerations with respet to ground. he harateristis of invoved methods are as foows: ) empoying MEMS aeerometers rather than gyro to ahieve the primitive features of gestures and aordingy inreasing the reiabiity as we as reduing osts; ) with reasonabe auray and effiieny the unit is easy to hod beause of aeerometers near-symmetria ayout.. Prinipes of Inertia Measurement When hand-hed unit moves in some writing pane with gestures rotationa and transationa motions are invoved in this proess whih an be sensed by inertia omponents. Normay Anguar rates and omposite aeerations are measured using gyro and aeerometer respetivey but an aternative approah exists: using severa aeerometers as the substitute for gyro to auate the anguar rates and then ahieving ground aeerations of the unit. egarding the hand-hed unit as a rigid body and attahing the body frame (O b X b Y b Z b ) to whih then the foowing radius vetor equation is satisfied for any point P in the unit: ' + L () where L and are the radius vetor of P reative to origins of body frame and inertia frame (O e X e Y e Z e ) respetivey is the radius vetor between origins of inertia and body frames. Differentiating this expression twie and using the theorem of Coriois we have de' de deω + L () + ω ( ω L) d ' where e d and e represent the aeeration at point P and the rotation enter in the order given d e ω and ω are the body s anguar aeeration and turn rate respetivey. For onstruting gyro-free inertia measurement unit we an mount more than one three-axis aeerometers at different positions of it the same amount of equations just ike eqn. () an be estabished simutaneousy whih are expeted to d provide supports for auating ω and e ' as we know that they ompose the primitive features of gestures. 3. Configuration of Aeerometers wo triaxia MEMS aeerometers an be mounted aong the unit s major axis nearsymmetriay as depited in Fig.. aeerometer Y b Z a O a X a Y a Z b O b Fig.. Configuration sheme of dua MEMS aeerometers. aeerometer Z a O a X a Y a he body frame O b X b Y b Z b has its origin at the prospetive hand-hed position and O b X b is in diretion of the unit s major axis. wo sensors with a sensitive axes aigned with axis set of body frame are oated on different side of O b from whih the distanes to them are and. Notie that is not equa to usuay beause the hand-hed position may vary at random but foowing anaysis wi prove that this situation doesn t affet the ahievement of gestures features. X b 35

3 Sensors & ransduers Vo. 7 Issue 5 May 04 pp When we impement above sheme two aeerometers an be mounted at the ends of handhed devies speifi SoC hip with F interfae shoud be paed at the entra position for samping auating and ommuniation. Beause the devie is sma and narrow just ike a pen hoding it by hand is very onvenient. 4. Measuring Gestures For measuring gestures we need to auate rotation anguar rates attitude of devies (desribed with diretion osine matrix) and finay get aeeration of gestures with respet to the oa geographi frame. A these tasks an be ahieved using speifi fores provided by the sensors whih aow eqn. () to be satisfied. 4.. Cauating Ground Aeerations By pre-mutipying both sides of equation () by the diretion osine matrix (denoted by C) a the terms an be rewritten with respet to the body frame. We get: db' db + ω L + ω ( ω L) (3) Assuming gravity vetor is G[00-g] beause the speifi fores provided by both aeerometers F and F aow foowing equation to be satisfied: Denoting ground aeeration at the position of one of the two aeerometers (for exampe aeerometer where an be seen as the nib of a pen) by a beause foowing reationship: is aways satisfied we get: d b de C a CF + G Combining above equations yieds: a CF + G F F I C + ω ω ( ω I) C C Ω where Ω is the 3 3 matrix and 0 ωz ωy Ω ωz 0 ω X ωy ωx 0 (7) (8) Equations (7) indiate that estimating ground aeerations reated to gestures reies on the omputation of anguar rate ω. d b ' + C F G (4) 4.. Cauating Anguar ates substituting for eft item of equation (3) yieds: and F F d (5) + ω ( ω L ) C G b + ω L b + ω L d (6) + ω ( ω L ) C G ewriting terms of Equation (7) in omponent form namey F [f X f Y f Z ] F [f X f Y f Z ] and ω[ω X ω Y ω Z ] then the seond equation an be expressed as foows: fz fz ωy + ωxωz + fy f Y ωz + ωxωy + fx fx ωy + ωz + where L [ 00] and L [ 00]. Subtrating equation (6) from equation (5) yieds: F F ω ω ( ω I) I C + For eah samping period terms f f f f f f x x Y Y Z Z where I[00] is unit vetor aong axis O b X b of the body frame. are a onstants. Denoting them by C X C Y and C Z respetivey yieds 36

4 Sensors & ransduers Vo. 7 Issue 5 May 04 pp ωy ωxωz + Z ωz ωxωy + Y (9) ωy + ωz X where ωy() i ( ωy() i ωy( i ))/ ωz() i ( ωz() i ωz( i ))/ he foowing equation may be derived by differentiating the third item in equation (9): where ωω + ωω / (0) Y Y Z Z X () i ( () i ( i ))/ X X X in whih is the samping period. Substituting for ω and ω in Eqn. (0) gives: Y ω + ω Z Z Y Y Z X / hen we get a set of simutaneous equations: ω + ω ω Z Y Y Z X Y + ωz X / () Equation () shows that the soution happens to be the intersetion of a ine and a ire. So ω Y and ω Z an be determined as foows: ± ( + ) ωy ( + ) ωz X Z Y X Y Z X ( Y + Z) X Y Z X Y Z X ( Y + Z) () Further more foowing equation an be derived from equation (9) and (): ω (( ω ) + ( ω ) ) / X Y Z Z Y X where the symbo of ω X an be determined aording to the ange between foowing vetors: Hene [ ωz ωy] [ ω ω ] ω X is given by: Y Z Z Y ( ω ) + ( ω ) ωx sgn X sgn / Y Z Z Y (3) Aording to equation (3) there are two aternative soutions exist. How to determine the unique one an be seen as a funtion regression probem whih refers to tasks of searhing the optimum soution in a given spae. Considering ω as a random vetor and defining an energy funtion: ω ωx + ωy + ωz hen it is reasonabe to assume that soution ω min whih ensures minimizing ω may be the optimum one. Beause reationship ω Y +ω Z X is satisfied and X is a onstant for any samping period the objetive funtion min ω is equivaent to min ω X and then the best estimation of anguar veoities an be done by soving the foowing optimization probem: min ω X st.. ( ω ) + ( ω ) ω X sng X XZ ± Y X( Y + Z) X ωy ( Y + Z) XY Z X( Y + Z) X ωz ( Y + Z) sng / Y Z Z Y From above anayses foowing agorithm for auating anguar rates an be proposed: For every samping period we do: Step : auate X Y and Z from F and F ; Step : obtain two groups of ω Y ω Z aording to equation (); Step 3: based on equation (3) two soutions of ω X are obtained and then we get two aternative soution vetors: ω and ω ; Step 4: from ω and ω the optimum soution is determined by verifying whether the objetive funtion min ω X is satisfied Error Compensation Normay zero and random drifts of MEMS aeerometers exist so there are onstant and random errors invoved in the vaues of X Y and Z whih wi affet the auating preision of anguar 37

5 Sensors & ransduers Vo. 7 Issue 5 May 04 pp rates. For dereasing these errors we empoy the Kaman stat estimation method to fufi the error ompensation for X Y and Z. Defining stat variabe Ct () ( () t () t ()) t X Y Z as the atua vaue orresponding to measured vaue: Ct () ( () t () t ()) t X Y Z then foowing reationship is satisfied: Ct () Ct () + E() t + E() t (4) where E (t) and E r (t) denote onstant and random error respetivey at time t: E() t ( ex() t ey() t ez()) t E ( t) ( e ( t) e ( t) e ( t)) r rx ry rz Equation (4) is satisfied at time t- as we so Ct ( ) Ct ( ) + E ( t ) + E ( t ) r r (5) Combining equation (4) and (5) and rearranging yieds: Ct () Ct ( ) + Ct () Ct ( ) + E ( t ) E ( t) + E ( t ) E ( t) r r Aording to equation (6) and (7) the optimum estimations of X Y and Z an be ahieved by exeuting Kaman fitering agorithm. 5. Experimenta Anayses In order to verify above sheme of dua aeerometers and reated agorithms we onduted an evauation of auating preision about anguar rates under noise-free and noise environment and experiments of gesture-based figure reognition. 5.. Anguar ates egression ests Assuming gesture satisfies the foowing mode: ωx ( t).5sin(5 t) ω y () t os(4) t ωz () t *sin(3) t ax () t 3sin() t ay () t 3os(8)os(4) t t az 4os(8 t)os( t) where anguar rates and aeerations are measured in rad/s and m/s respetivey 0.04m samping period is 5 ms. he fitting urve between auated and rea anguar rates aong X Y and Z axis are depited in Fig. Fig. 3 and Fig. 4. For onstant errors E (t)- E (t-)0 are aways satisfied; meanwhie the differene between two white Gaussian noise signas is sti white Gaussian noise. So we assume W(t)E r (t-)- E r (t) the above equation an be written as foows: Ct () Ct ( ) + Ct () (6) Ct ( ) + Wt ( ) whih is the system state equation. Beause N E () t C()/( i N* ) i Fig.. ωy resoving deviation. if we assume Yt () Ct () E() t the system measurement equation an be derived: Yt () Ct () + E() t (7) r From Fig. and Fig. 3 we an see that ω Y and ω Z an be rebuit auratey (Fig. () Fig. 3 ()) from two aternatives (Fig. (a) Fig. (b) Fig. 3 (a) and Fig. 3 (b)). At very few points aong time axis disagreements between estimated and rea vaues exist this is aused by auating errors (referring to Eqn. () if denominator beomes zero namey ω Y +ω Z 0 errors wi inrease). 38

6 Sensors & ransduers Vo. 7 Issue 5 May 04 pp Fig. 3. ωz resoving deviation. data (whih has been reverse engineered by the opensoure ommunity). For impementing our sheme we butt two Wii Controer together aong their major axis. Aording to the physia paement two aeerometers are 0. m apart with a sensitive axes aigned. As extra omponents gyro sensors are used to verify the preision of auated anguar rates and trigger-stye button B on the bak of the ontroer is used to trigger and stop the samping proedures (whih approximatey keep ative for seonds). eated agorithms of omputing gestures traks are impemented in Matab environment. In aordane with the methods desribed in setion 3 we firsty exeute Kaman fitering agorithm and then auate anguar rates and ompare whih with gyro outputs. Fig. 5 shows the fitting urve between measured estimated vaues of X Y and Z and idea ones auated based on gyro outputs when we write 8 with gesture. It an be seen that the fitting urves of estimated data are we onsonant with what auated from gyro outputs whih proves the system state & measurement equations are effetive. Fig. 4. ωx resoving deviation. Fig. 4 (a) shows that auating errors of ω X are bigger than ω Y and ω Z. Comparing with Fig. and Fig. 3 we an find the points at whih errors exist onsist with where errors of ω Y and ω Z appear. his an be attributed to the auating proess of ω X whih reies on the derivative of ω Y and ω Z namey itte error of ω Y and ω Z wi resut in bigger one after derivation. Beause these points are sparse orresponding errors an be eiminated as the high frequeny-segments by ow pass fitering. he fina resut fits atua vaue we (Fig. 4 (b)). 5.. Gestures raks eovering ests For the further performane determination of reated methods presented in setion 3 and 4 under noise environments we made a figure-aimed reognition test based on our methods. Preparing the evauation we use Nintendo Wii Motion Pus Wireess Controer as our input devie [3] whih inorporates a triaxia MEMS aeerometer a dua-axis tuning fork gyro and a singe-axis gyro. Conneted to PC instead of gaming onsoe via the Buetooth Human Interfae Devie (HID) protoo It is possibe to readout a sensors Fig. 5. Effets of Kaman state estimation. abe ists orreation oeffiients between auated anguar rates and gyro outputs with regard to gestures about figures 0-9. esuts show that they are highy orreated (for a figures r>0.85) whih indiates the ombination of fitering and suedent resoving agorithms work we. Furthermore we an see that orreation degrees about ω X are ower than about ω Y and ω Z whih an be attributed to derivation operations this is onsistent with the onusions in setion 5.. For observing gestures traks of figures 0-9 we firsty get diretion osine matrix by integrating anguar rates inear aeerations and then threedimensiona traks subsequenty the panar traks are ahieved by exeuting dimensionaity redution with PCA-based methods [4] whih are shown in Fig

7 Sensors & ransduers Vo. 7 Issue 5 May 04 pp esuts show that there are some adjoining or distortiona strokes in these traks beause no referenes and feedbaks exist among gesture proesses but they are suffiient grounds for subsequent pattern reognitions. abe. Correation oeffiients between resoving and gyrosope samping vaues. Char ωx ωy ωz Conusions Fig. 6. Gesture traes of figures. In this paper we proposed a design of miro inertia measurement unit for gesture-based interfae whih is haraterized by the onfiguration of dua MEMS aeerometers and the agorithm for auating anguar rates and inear aeerations. he near-symmetria ayout of two triaxia MEMS aeerometers promises the unit is sma and onvenient for hoding; meanwhie orresponding agorithm has simpe form for auating anguar rates by using an energy funtion we an ahieve an estimation of time series about anguar rates auratey. Due to anayti instead of integration methods umuative errors are not invoved in auating anguar rates proess; Kaman fitering for arguments denoising ontributes to improve resoving preision further. Preiminary experimenta verifiation shows that a these sheme and methods are reasonabe and feasibe. eferenes []. Sushmita Mitra inku Aharya Gesture reognition: a survey IEEE ransations on System Man and Cybernetis Vo. 37 Issue pp []. I. J. Jang W. B. Park Signa proessing of the aeerometer for gesture awareness on handhed devies in Proeedings of the IEEE Internationa Workshop on obot and Human Interative Communiation oman Otober November 003 pp [3]. J. Kea P. Korpipaa D. Mara Aeerometr-based gesture ontro for a design environment Persona and Ubiquitous Computing Vo. 0 Issue pp [4]. Sven Kratz Mihae ohs Georg Ess Combining aeeration and gyrosope data for motion gesture reognition using assifiers with dimensionaity onstraints in Proeedings of the Internationa Conferene on Inteigent User Interfaes (IUI 3) Santa Monia USA 9- Marh 03 pp [5]. homas Shomer Benjamin Poppinga Nies Henze and Susanne Bo Gesture reognition with a Wii ontroer in Proeedings of the nd Internationa Conferene on angibe and Embedded Interation (EI 08) Bonn Germany 8- February 008 pp. -4. [6]. L. D. DiNapoi he measurement of anguar veoities without the use of gyros he Moore Shoo of Eetria Engineering University of Pennsyvania Phiadephia 965. [7]. A.. Shuer Measuring rotationa motion with inear aeerometers IEEE ransations on Aerospae and Eetroni Systems Vo. 3 Issue pp [8]. S. J. Merhav A nongyrosopi inertia measurement unit Journa of Guidane Contro and Dynamis Vo. 5 Issue 3 98 pp [9]. Sou-Chen Lee Liu Cheng-Yu An innovative estimation method with own-ship estimator for an a aeerometer-type inertia navigation system Internationa Journa of Systems Siene Vo. 30 Issue 999 pp [0]. Yue Peng Shi Zhen Gyro free inertia navigation system based on MEMS aeerometer Journa of Chinese Inertia ehnoogy Vo. 9 Issue 0 pp []. Xue Yang Jin Lian-Wen A feature extration and reognition approah for aeerometer based virtua handwriting digit Pattern eognition and Artifiia Inteigene Vo. 4 Issue 4 0 pp []. Xue Yang Human motion patterns reognition based on singe triaxia aeerometer Shoo of Eetroni and Information Engineering South China University of ehnoogy Guangzhou 0. [3]. Nintendo Web Porta ( [4]. Ian Joiffe Prinipa omponent anaysis Brian Everitt John Wiey & Sons Copyright Internationa Frequeny Sensor Assoiation (IFSA) Pubishing S. L. A rights reserved. ( 40