Front-Crawl Instantaneous Velocity Estimation Using a Wearable Inertial Measurement Unit

Transcription

1 Sensors 2012, 12, ; doi: /s Aricle OPEN ACCESS sensors ISSN Fron-Crawl Insananeous Velociy Esimaion Using a Wearable Inerial Measuremen Uni Farzin Dadashi 1, *, Floren Creenand 2, Grégoire P. Mille 2 and Kamiar Aminian Laboraory of Movemen Analysis and Measuremen, École Polyechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Swizerland; kamiar.aminian@epfl.ch Insiue of Spor Sciences, Universiy of Lausanne, 1015 Lausanne, Swizerland; s: floren.creenand@unil.ch (F.C.); gregoire.mille@unil.ch (G.P.M.) * Auhor o whom correspondence should be addressed; farzin.dadashi@epfl.ch; Tel.: ; Fax: Received: 31 July 2012; in revised form: 17 Sepember 2012 / Acceped: 17 Sepember 2012 / Published: 25 Sepember 2012 Absrac: Monioring he performance is a crucial ask for elie spors during boh raining and compeiion. Velociy is he key parameer of performance in swimming, bu swimming performance evaluaion remains immaure due o he complexiies of measuremens in waer. The purpose of his sudy is o use a single inerial measuremen uni (IMU) o esimae fron crawl velociy. Thiry swimmers, equipped wih an IMU on he sacrum, each performed four differen velociy rials of 25 m in ascending order. A ehered speedomeer was used as he velociy measuremen reference. Deploymen of biomechanical consrains of fron crawl locomoion and change deecion framework on acceleraion signal paved he way for a drif-free inegraion of forward acceleraion using IMU o esimae he swimmers velociy. A difference of 0.6 ± 5.4 cm s 1 on mean cycle velociy and an RMS difference of 11.3 cm s 1 in insananeous velociy esimaion were observed beween IMU and he reference. The mos imporan conribuion of he sudy is a new pracical ool for objecive evaluaion of swimming performance. A single body-worn IMU provides imely feedback for coaches and spor scieniss wihou any complicaed seup or resraining he swimmer s naural echnique. Keywords: acceleromeer; gyroscope; biomechanical consrain; srap-down inegraion; swimming velociy

2 Sensors 2012, Inroducion The adven of new echnologies has changed he percepion of ahleic achievemen. In swimming, he narrow gap beween record holders, poins o he growing imporance of devising new ools o assess self-improvemen and opimize he raining process. However, he biomechanical analysis of swimming remains inadequaely explored due o complicaions of kinemaics measuremens in waer. To dae, he mos common pracice for performance monioring in swimming is using video-based sysems. A video sequence is capured and pos-processed hrough digiizaion [1,2]. The main downside of such sysems is being excessively ime consuming and problemaic o fully auomae. The applicaion of his class of mehods can be severely resriced by facors such as ligh refracion in waer or bubbles generaed around he swimmers bodies [3]. Recenly a markerless 3D analysis mehod was proposed [4] based on exracion of a swimmer s silhouee. This mehod reduced he video processing ime, while sill being sensiive o differen lighing condiion ha leads o misidenificaion of feaures [5]. The second caegory of echniques uses ehered monioring. An early version of such a sysem was developed by Craig e al. [6]. Velociy is direcly measured by a cord aached o he swimmer. The cord is ehered o a poolside shaf-encoder [7,8]. Alhough his sysem is considered as reference o assess swimming velociy, he device disurbs he swimmers echnique and measures he velociy only in he forward direcion. Moreover, he sysem requires a resising force o ighen he cord during he deceleraions of swimmer for an accurae measuremen. Hence, his force is consanly applied o he swimmer. During he pas wo decades inerial measuremen unis (IMUs) have been proven o be powerful ools in human movemen analysis [9]. Firs and foremos he porabiliy of IMUs made hem a viable sysem in daily life measuremens, conrary o mos oher measuremen sysems which are resriced o laboraory condiions. Besides, he echnological developmens in microelecromechanical sysems (MEMS) have made IMUs a low cos opion compared o in-laboraory seings. The applicaion of IMUs for spor analysis is a new rend in spor biomechanics [10 12]. A considerable number of sudies have been conduced on he applicaion of IMUs in he swimming conex. Chronologically, Ohgi e al. [13] were probably he firs o use a wris-worn IMU o deec fron crawl and breas sroke swimming phases auomaically. A sacrum mouned 3D acceleromeer was used by Davey e al. [14] o auomaically exrac simple merics such as lap ime and sroke rae. An IMU comprising a 3D acceleromeer, 2D gyroscope and RF ransceiver was used by Le Sage e al. [15] o characerize swimming srokes in real ime. However, none of aforemenioned works involved kinemaic measuremens using IMUs. Recenly, Samm e al. [16] published a mehod using a 3D acceleromeer on he lower back o measure he fron crawl velociy. However, a single 3D acceleromeer generally is no capable of measuring he orienaion of he body during dynamic movemen. Consequenly, he effec of laeral and verical acceleraion of swimmer s body canno be removed from acceleraion in he forward direcion of swimming, herefore, calculaing he inegral of he acceleraion signal in [16] o evaluae he velociy can be misleading. Besides, i is well known ha he accuracy of IMU-based sysems in velociy measuremen rapidly degrades over ime due o inheren sensor noises [17]. Hence special consideraions are needed for a reliable assessmen of velociy.

3 Sensors 2012, Considering he velociy as he mos inuiive meric of swimmers performance, his sudy aimed o propose a new mehod o measure swimming velociy in fron crawl, using a single body-worn inerial sensor. We hypohesize ha he swimmer s insananeous velociy can be esimaed accuraely from IMU measuremens when he average velociy of he swimmer over he rial is known. Drif-free inegraion of acceleraion was cerified in his sudy by assuming some simple locomoion consrains of he fron crawl. Experimenal proocols and saisical ools are inroduced o assess he validiy of he cycle and insananeous velociy esimaion mehod. 2. Experimenal Secion 2.1. Paricipans and Proocol Eleven elie and nineeen recreaional swimmers ook par in his sudy. Their aribues are shown in Table 1. Each paricipan was informed of he procedures and risks associaed wih sudy paricipaion and gave wrien informed consen prior o paricipaion. This sudy was performed in accordance wih he Declaraion of Helsinki and was approved by he Ehics Commiee of he Faculy of Biology and Medicine, Universiy of Lausanne (proocol #87/10). Each swimmer performed consecuive 25 m fron-crawl rials in four differen increasing velociy rials from 70% o 100% of heir bes personal 100 m iming recorded one monh before he measuremen. In case he performance ime was differen more han ±5% from he argeed ime, he swimmer repeaed he rial. They were asked o posiion in he waer a he edge of he pool for sars. Table 1. Saisics of he measuremen populaion. All variables are presened as mean ± sandard deviaion. V 100 shows he average of bes personal 100 m iming. Group Male Female Age (yrs) Heigh (cm) Weigh (kg) V 100 (m/s) Elie ± ± ± ± 0.17 Recreaional ± ± ± ± Daa Acquisiion and Calibraion The swimmers were equipped wih one waerproofed inerial sensor (Physilog, BioAGM, La Tour-de-Peilz, Swizerland) including a 3D acceleromeer (±11 g) and a 3D gyroscope (±900 /s) and embedded daa logger recording a 500 Hz. The sensor was worn on he sacrum inside he pocke of a cusom designed swimming sui wih a Velcro closing as shown in Figure 1. According o he feedback from swimmers, by wearing he sensor aachmen in our sudy hey did no feel he IMU imposed a noiceable drag during heir raining. The sensor was calibraed for offse, scale and non-orhogonaliy using in-field calibraion procedure [18]. As reference sysem, a ehered apparaus (SpeedRT, ApLab, Rome, Ialy) [8] was aached o he wais of swimmers jus beneah he lower end of he sensor wih a bel. The sysem calculaes he velociy by measuring he cord displacemen hrough ime a 100 Hz recording. The resisance applied o keep he cord igh is adjusable via a cluch on he pulley comparmen of he apparaus. In our measuremen, he resisance was se o 500 g [19]. Since he ehered reference is insalled on he saring block above he swimming level, he SpeedRT cord is no parallel o he direcion of

4 Sensors 2012, swimming and imposes he parallax problem [15]. By knowing he cord displacemen a each ime insan and he fac ha he reference pulley was posiioned 72 ± 1 cm above sill pool waer level, we calculaed he insananeous velociy measured by he reference in he swimming direcion Esimaion of Swimming Orienaion Using IMU Insananeous velociy is esimaed by inegraing he forward acceleraion signal in he global frame (GF: X, Y, Z) (Figure 1). Among he axes of GF he Z is assumed o be verically upward and Y in parallel wih he longiudinal edge of he pool. The acceleraion in GF can be calculaed from he acceleraion measured in sensor frame (SF: x, y, z) by considering he orienaion of SF relaive o GF a each ime sample. The following paragraphs describe he required seps. Figure 1. The inerial sensor wih waer proofing box and is placemen. The global frame SF GF (GF: X, Y, Z) and he sensor frame (SF: x, y, z) and relaive quaernion q ha represens sensor frame daa in he global frame is also shown. By saring he rials from a relaively moionless posure in waer, he iniial sacrum acceleraion SF x y z T a0 a0, a0, a 0 has a magniude equal o he graviy. Using quaernion based algebra o represen he orienaion, he iniial quaernion which aligns he z axis o Z, is given by: q cos, u SF GF sin 2 u0 2 (1) where,. represens Euclidian norm, θ 0 is he iniial inclinaion and u 0 represens he horizonal axis around which he roaion is done. Supposing ha azimuh angle a sar of rial is null, θ 0 and u 0 can be calculaed as in Equaion (2) and Equaion (3), respecively:

5 Sensors 2012, SF GF 0 cos ( a0. Z ) (2) SF GF y x u0 a0 Z a0, a0,0 (3) where represens he normal cross produc. SF GF A each ime sep, he orienaion of SF relaive o GF, q is updaed using he previous SF x y z T orienaion by inegraing he angular velociy,, [20]: q SF SF SF SF GF SF GF cos, sin q SF 1 2f 2f where f is sampling frequency and indicaes quaernion muliplicaion. The ime inegraion in Equaion (4) suffers from an accumulaive drif [17] due o gyroscopic noise. In order o reduce he effec of his drif we applied a dynamic biomechanical consrain, namely considering he swimmer sacrum rolls in average abou forward direcion Y. Therefore, for he daa samples from cycle k o k + 1 (denoed by C and C k+1 respecively), he principal componen of angular velociy in GF (represened by wrien as: k (4) ) should be aligned o Y. This can be mahemaically 1 P principle componen q q 0,1,0 : C C (5) GF SF GF SF SF GF k k1 Figure 2. Angular velociy in GF and represenaion of biomechanical consrain for orienaion correcion. Principle componen of angular velociy in he global frame ( ) and is deviaion from forward axis of he movemen ( ) are shown. Any deviaion from he condiions of Equaion (5) was assumed o be he effec of he orienaion drif. Figure 2 shows he deviaion of one cycle from his condiion. The ampliude of he drifed angle is given by Equaion (6):

6 Sensors 2012, GF 0,1,0. P 1 cos GF P Accordingly he roaion axis is presened as in Equaion (7): u (6) GF 0,1,0 PC k GF (7) P So if we suppose ha he drif is linearly increased hrough one cycle wih n daa poins, for he h sample we can compue he correcive quaernion as in Equaion (8): u q C C 2( n1) u 2( n1) C k cos ( 1), sin ( 1) : k k 1 Therefore, he correced orienaion of SF relaive o GF, SF GF C, k SF GF SF GF, (8) q can be calculaed from Equaion (9): q q q (9) The insananeous forward acceleraion in global frame can be calculaed according o Equaion (10), where shows he graviy vecor: 2.4. Insananeous and Cycle Velociy Esimaion 0 1 Y SF GF SF SF GF a q, C a,. 1 k q C g k 0 The insananeous velociy V can be obained by rapezoidal inegraion of a Y. Neverheless, his operaion is no drif-free and resuls in a slow gradual rend in he cycle mean velociy. This velociy drif should be discriminaed from he acual change originaing from body acion which accompanies a change in acceleraion ampliude. Therefore, he forward acceleraion a Y is divided ino segmens where he range of acceleraion remains wihin he same inerval. Subsequenly, a each segmen we filer ou he velociy drif. We used he geomeric moving average (GMA) change deecion algorihm [21] for a Y segmenaion. The algorihm is based on recursive esimaion of signal variance and deecing if he variance change exceeds a predefined hreshold. The hreshold was seleced empirically as 20% of he a Y variance. Much smaller hresholds end up o deecion of spurious signal segmens while higher hresholds canno recognize any changes of swimming regime. Figure 3(a) illusraes he resul of his segmenaion. For velociy drif removal, we assumed he average rend of V peaks wihin each segmen is quasi-consan due o he seady regime of swimming. Therefore, a each segmen, cycle minimum and maximum peaks of V were exraced and a shape preserving spline [22] was fied o hese peaks [23]. De-rending was done by subracing he average of upper and lower rend curves from he original velociy curve. Figure 3(b) depics he exracion of he rend paern. The insananeous velociy curve hen will be correced for rial mean velociy by assuming ha he average velociy of he rial is known from lengh of he pool and he duraion of each rial. Finally, was esimaed as he mean (10)

7 Sensors 2012, value of V for each cycle C k. The algorihm developmen phase was compleed by using he daa of only 10 swimmers and hen our algorihm was applied o he enire daa se (30 swimmers). Figure 3. Inermediae seps of velociy profile calculaion (a) Geomeric moving average (GMA) change deecion on forward acceleraion variance. The acceleraion signal is segmened in hree pars and correcion is applied separaely o each par. (b) Spline fiing on upper and lower peaks of he firs segmen acceleraion (dash-do lines) and velociy drif paern (dashed line) Saisical Analysis A wofold validaion of he proposed velociy esimaion mehod is presened in his secion. In he firs sep, we provided he saisics o assess he cycle mean velociy esimaed using our sysem ( ). To his end, he mean (accuracy) and sandard deviaion (precision) of he difference beween measured by SpeedRT sysem and obained from IMU,, was calculaed for differen rials of each subjec. Spearman s rank correlaion was also used o verify he associaion beween he wo sysems. Agreemen beween he wo sysems in measuremen was assessed by use of Bland-Alman plo [24] and normalized pairwise variabiliy index (npvi) [25] as calculaed by Equaion (11): SRT IMU N V V npvi 100% N SRT IMU 1 V V 2 (11) C k where N is he oal number of sudied cycles. The Bland-Alman plo was inspeced wih correlaion exploraion for exisence of heeroscedasiciy [26]. In he second sep we invesigaed he efficiency of our mehod in measuring he insananeous velociy. The roo mean squared (RMS), maximum and corresponding relaive error of insananeous velociy was calculaed. As hese calculaions require similar ime sampling of proposed and reference sysems, he insananeous velociy curve calculaed by our mehod was downsampled o 100 Hz prior o error calculaions. Besides, an indirec measure of accuracy of our sysem in insananeous velociy measuremen was provided by assessmen of inra-cyclic velociy variaion (IVV). In fac, he concurren validiy of our mehod was assessed by invesigaing IVV of he wo groups of swimmers (Elie and Recreaional), esimaed by he wo sysems. IVV is compued as in Equaion (12):

8 Sensors 2012, IVV C 1 1 C 1 1 V V f n 2 V f n (12) where represens cycle frequency, C is he number of cycles in he rial and n is he number of rial samples [27]. We performed a hree-way repeaed ANOVA (significance level of p < 0.01) o examine he effec of rial, group and measuremen device on IVV. 3. Resuls and Discussion We have proposed a new wearable sysem and dedicaed algorihms o measure fron crawl velociy and described is validaion procedure agains a reference ehered device. Figure 4 illusraes a ypical resul of he insananeous velociy obained wih our mehod and he reference sysem. A oal number of N = 1,448 cycles were compared beween he wo sysems. Figure 4. A ypical resul of velociy calculaion using IMU (Solid line) compared o he reference ehered apparaus (doed line). A significan correlaion was observed beween he wo sysems (Spearman s rho = 0.94, p < 0.001) in assessmen. The and he differed by 0.6 cm s 1 and he precision was 5.4 cm s 1 ( range [0.91, 1.95] cm s 1 ). Table 2 summarizes he comparison beween he wo sysems for all four differen ranges of mean velociy (as measured by he reference and IMU). The resuls demonsrae ha he proposed sysem is capable of measuring fron-crawl velociy wih accepable accuracy (below 1.1 cm s 1 ) and precision (below 5.8 cm s 1 ) suggesing ha our mehod can be reliably used for cycle mean velociy measuremens. This accurae esimaion of sroke cycle velociy was possible hanks o: (i) sensor orienaion drif removal in GF using he principal componen of swimming kinemaics; (ii) velociy drif removal by inroducing an appropriae segmenaion of forward acceleraion and by a spline shape modeling of he drif a each segmen afer inegraion of acceleraion. The wo sysems differed by 3.5% in assessmen of variaions as presened by npvi in Table 2. The npvi values in Table 2 shows ha he difference in variabiliy assessmen of beween he wo

9 Sensors 2012, sysems in four ranges of velociy is less han 3.9%. This resul as well as high correlaion beween he wo sysems confirms ha our mehod deecs he changes similar o he reference and suppors he validiy of our esimaion. Table 2. Average velociy of he rials as measured by he wo sysems are shown under Measured Mean Velociy column. Cycle mean velociy ( ) difference beween he reference and IMU in differen rials is shown in column labeled Evaluaion of. The variaion difference wih he reference is presened in erms of normalized Pairwise Variabiliy Index (npvi). Number of Measured Mean Velociy Evaluaion of Cycles Reference (m s 1 ) IMU (m s 1 ) Error (cm s 1 ) npvi (%) Trial ± ± ± Trial ± ± ± Trial ± ± ± Trial ± ± ± Toal ± ± ± V C k Figure 5. Bland-Alman plo, represening mean (x-axis) and difference (y-axis) beween he values esimaed by body-worn IMU and reference ehered apparaus (SpeedRT). Limis of agreemen (do lines) are locaed a mean difference ±1.96 sandard deviaion of he difference. The Bland Alman plo showed he 95% limis of agreemen lower han 10.8 cm s 1 beween he wo sysems in assessmen as depiced in Figure 5, where no significan difference and no heeroscedasiciy (correlaion = 0.03) were found. This finding, implies uniform performance of he mehod hroughou he sudied range of. I is noeworhy ha by using he prior informaion abou pool lengh o correc he velociy profile an error of 10.4 ± 39.7 cm is observed in esimaing he sacrum s displacemen. This error was expeced since he sacrum does no necessarily ravel a complee lengh of he swimming pool.

10 Sensors 2012, As regards validaion of insananeous velociy, an RMS difference of 11.3 cm s 1 was observed ha is comparable o he precision of he reference sysem. The maximum insananeous error was 18.2 cm s 1 ha corresponds o a relaive error of 9.7%. One source of he difference beween he velociy esimaed by our mehod and he velociy measured by he reference is a small arifac due o he non-rigidness of he swimming sui. Neverheless, he cusom designed swimming sui used o fix he sensor did no allow he sensor o move drasically and kep he arifac wihin a olerable range. Moreover, during high acceleraions when he arifac is more pronounced, he random bias of acceleromeer is less significan (higher signal o noise raio) which leads o accepable resuls [28]. Indirec validaion of insananeous velociy by IVV in Table 3 hrough four differen velociy ranges and he wo differen groups of paricipans, suggess ha he IMU can be used for he sudy of insananeous velociy variaions. Indeed, our sysem, in accordance wih he reference, showed a significan difference (p < 0.01, p < 0.001) o discriminae elie and recreaional group based on IVV values (in differen ranges of velociy). The reference showed an IVV change from 13.7% o 17.5% for he elie group and from 19.6% o 23.3% for he recreaional group. Our mehod in accordance wih he reference, showed significanly lower IVV values for elie swimmers (Table 3) ha is consisen wih previous sudies [7,29]. Table 3. Comparison of inra-cyclic velociy variaion (IVV) beween he wo sysems for elie and recreaional groups in differen rials. a p < 0.01 and b p < 0.001: significan difference beween IVV of he wo groups for he same measuremen sysem. * p < 0.001: significan difference beween he wo sysems in IVV assessmen. Group Number of Reference (%) Inerial (%) IVV Error (%) Cycles Mean Sd Mean Sd Accuracy Precision Trial1 Elie a a * 1.7 Recreaional a a Trial2 Elie b b * 2.3 Recreaional b b * 3.5 Trial3 Elie * 3.1 Recreaional Trial4 Elie b b * 2.1 Recreaional b b * 4.0 Anoher observaion from Table 3 is ha he IMU ends o underesimae he IVV as presened by posiive error values. However, he ANOVA shows ha he small sysemaic difference beween he wo sysems is no affeced by group facor (p > 0.3). In a nushell, using IMU he same sysemaic error can be seen for differen groups of swimmers and can be compensaed. The abiliy of he inerial sensor o disinguish he variabiliy of he movemen of he subjecs wih differen performance levels propounds he applicaion of he inerial sysem in he sudy of swimming velociy. The capaciy of our sysem o deec IVV changes also provides imporan evidence ha our velociy drif removal mehod does no cancel ou he velociy variaions. Indeed, differen swimming rial regimes were recognized based on changes of acceleraion magniude. These regimes are reaed separaely o miigae he effec of he velociy drif and hereof variaion of velociy signal was well mainained.

11 Sensors 2012, Signal segmenaion using GMA is he core of drif removal in our mehod. Therefore, invesigaing he effec of changing he segmenaion hreshold in GMA can be illusraive of he mehod s robusness. To his end, he hreshold in he GMA algorihm was shifed 5%. The effec of his change on he esimaion is shown in Table 4. I can be seen ha a decremen of 5% in he hreshold led o a bigger error in he esimaed velociy han equal incremen. The small hreshold caused many spurious segmens on he a Y signal which resuled in excessive localized correcion on he velociy paern; on he conrary, since during 25 m laps he acual acceleraion profile of he swimmers does no change frequenly, he higher hreshold did no noably cu down on he algorihm performance. Table 4. The effec of changing he segmenaion hreshold of geomeric moving average (GMA) by a facor of 5% on velociy esimaion. Esimaion error in he cycle mean velociy (MEAN ± SD) and insananeous velociy (RMS) are presened. GMA Threshold Velociy Esimaion Error (cm s 1 ) Cycle Mean ( ) Insananeous 0.15 var(a Y ) 0.3 ± var(a Y ) 0.5 ± Our daase includes only one ype of iniial condiion (swimming sars from a relaively moionless posure in waer followed by a wall push) ha is a subse of possible iniial condiions in swimming. However, he sudy of oher iniial condiion was no feasible wihin he scope of our experimen for pracical reasons. Since he ehered reference only measures he velociy in forward direcion of swimming, comparison of he muli lap daa wih urns beween he IMU and he ehered device was no realizable. Alhough diving from he sar block was a possibiliy, we avoided i for wo pracical consideraions. Firsly, during he diving period calculaion of he parallax effec on he velociy measured by he ehered reference is no possible. Secondly, avoiding he dives we could collec more sroke cycles which augmens he saisical power of our sudy. The algorihm we proposed in his paper, despie providing imely resuls, should no be misinerpreed as being real ime. The daa sream of one complee lap serves as he inpu of our algorihm since he correcion is performed per lap. For a near real-ime implemenaion of our mehod a crucial sep is o deermine he cycle mean velociy wihou using prior informaion abou pool lengh. 4. Conclusions The proposed mehod presens a reliable IMU-based sysem ha can be pracically used o measure he swimming velociy as he mos inuiive meric of he ahlee s performance. The sysem is user-cenric meaning ha several ahlees can wear heir own sensor a a ime wihou inerfering wih he oher ahlees measuremens. Developmen of such a ool can help coaches pinpoin he srenghs and weaknesses of he ahlees during workou sessions and design an opimal personal raining plan for ahlees o improve heir performance. Accurae measuremen of swimming velociy allowed he assessmen of inra-cycle variabiliy, an imporan deerminan of swimming efficiency. Analysis of swimming velociy along wih oher parameers such as coordinaion [11] and energy expendiure can shed a new ligh on he biomechanics

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