Estimation of the Knee Flexion-Extension Angle During Dynamic Sport Motions Using Body-worn Inertial Sensors

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1 Estimation of the Knee Flexion-Extension Angle Duing Dynamic Spot Motions Using Body-won Inetial Sensos Caolin Jakob Patick Kugle Felix Hebensteit, Samuel Reinfelde Matthias Lochmann Ulf Jensen Bjoen M. Eskofie Dominik Schuldhaus Digital Spots Goup, Patten Recognition Lab, Depatment of Compute Science Institute of Spot Science and Spot Fiedich-Alexande-Univesity Elangen-Nuembeg, Gemany ABSTRACT Motion analysis has become an impotant tool fo athletes to impove thei pefomance. Howeve, most motion analysis systems ae expensive and can only be used in a laboatoy envionment. Ambulatoy motion analysis systems using inetial sensos would allow moe flexible use, e.g. in a eal taining envionment o even duing competitions. This pape pesents the calculation of the flexion-extension knee angle fom segment acceleation and angula ates measued using body-won inetial sensos. Using a functional calibation pocedue, the sensos ae fist aligned without the need of an extenal camea system. An extended Kalman filte is used to estimate the elative oientations of thigh and shank, fom which the knee angle is calculated. The algoithm was validated by compaing the computed knee angle to the output of a efeence camea motion tacking system. In total seven subjects pefomed five dynamic motions: walking, jogging, unning, jumps and squats. The aveaged oot mean squaed eo of the estimated knee angle was 8. ±.4 ove all motions, with an aveage Peason-coelation of.97 ±.. In the futue this will allow the analysis of joint angles duing dynamic spots movements. Keywods inetial sensos, feedback taining, spots, joint angles, motion tacking, Extended Kalman Filte, Eule angles.. INTRODUCTION Motion analysis has become an impotant tool, which can contibute to the pefomance of an athlete []. It obtains an objective chaacteistic of the motion, which is used to geneate qualitative feedback. Theeby, the pefomance of the athlete can be impoved while injuies can be avoided [6]. The analysis of athletes pefomance is usually done with a camea motion tacking system in a laboatoy envionment []. It is seen as the gold standad because of its high accuacy. Howeve, the camea motion tacking system is expensive and motion is pefomed in an atificial envionment, e.g. on a teadmill [6]. The disadvantages of a camea motion tacking system can be ovecome with inetial sensos. An inetial measuement system is ambulatoy, cheap and motion analysis can be pefomed outside a lab in a eal taining envionment o even duing competition [8]. Though thei low powe consumption, even long tem obsevations ae possible [8] and such systems have been used fo medical applications []. A set of thee-dimensional acceleometes attached on the human body can be used as an inclinomete to measue the oientation of sensos with espect to gavity [], []. With the use of models, joint angles can be estimated. The accuacy is less fo motions with elatively lage acceleations. Thee-dimensional gyoscopes can be incopoated to impove the accuacy [5], [6], []. The angula ates measued by the gyoscopes ae integated to estimate the change of oientation. Howeve, ove time, lage integation eo can accumulate. The acceleomete in combination with the gyoscope can be used to compensate the difts and to define an absolute oientation [6]. Besides deteministic appoaches as TRIAD (Ti-axial attitude Detemination) and QUEST (Quatenion Estimato), the pefeed choice to fuse measuements of acceleomete and gyoscope and to estimate human body oientation with a high accuacy is a stochastic appoach, the Kalman Filte [8]. Estimation of the thee-dimensional oientation of body segments using inetial sensos in combination with magnetic sensing, including a thee-dimensional acceleomete,

2 a thee-dimensional gyoscope and a thee-dimensional magnetomete, is available in eseach [8] and fo commecial systems [7]. In such a measuement system, the acceleomete is used to detect inclinations, the gyoscope to detect fast changes and the magnetomete to measue a hoizontal efeence diection. Unfotunately, the measuements of the magnetomete can be distoted in the poximity of feomagnetic mateials [6]. The calibation of the sensos attached on the human body can be done using an extenal system, i.e. a camea motion tacking system [] o a steeoscopic camea []. Fave et. al [5] poposed an alignment pocedue of sensos without the need of an extenal system. Two alignment motions ae used to align the sensos vetically and hoizontally. Howeve, they did not apply thei method to highly dynamic spot motions, e.g. jumping. The usage of inetial-based joint angle detemination system in the fields of spots is still an unexploed eseach aea. Chadonnes et. al [], e.g. established an application of inetial senso and knee angle detemination in alpine spots. An inetial senso mounted at the ankle was used duing unning in [9] to classify di eent unning sufaces and inclinations. Downling et. al [4] investigated the impovement of motions though feedback by inetial sensing fo avoiding anteio cuciate ligament injuy and Coope et. al [] evaluated an inetial-based knee angle estimation appoach fo slow jogging. The estimation of the knee angle in unning and futhe dynamic motions is still unexploed [8]. The pupose of this pape is to investigate the pefomance of an inetial-based oientation estimation appoach in highly dynamic motions. As the application is the usage in spots, the alignment of senso fames should be achieved without the usage of an extenal system. The idea of Fave et. al [5] is used fo calibation and the oientation estimation is done using an extended Kalman filte. As an example fo an impotant joint, we will focus on detemining the knee angle using an acceleomete and gyoscope attached to both the thigh and shank. In the following sections we give details on the used inetial measuement system, pesent the poposed algoithm fo estimation of the joint angle and evaluate ou system in an extensive study involving multiple dynamic motions.. METHODS The next sections outline the poposed method fo calculating the flexion/extension knee angle fom inetial senso data. Fist, we descibe how the sensos ae placed and which coodinate systems ae used to descibe the joint motion. Then we descibe the algoithm fo computing the knee angle, which consists of thee main pats. Fist the senso fames ae aligned using a functional alignment pocedue. As a second step, an extended Kalman filte (EKF) estimates the elative oientation of each IMU. Finally this infomation is combined in the flexion/extension knee angle calculation step. Figue illustates the main concept of the knee angle estimation pesented in this pape.. Desciption of Joint Motion Fo the calculation of the knee angle we assume that two IMUs containing D acceleometes and D gyoscopes ae attached to the thigh and shank (see Figue ), foming two senso fames UVW and uvw. The knee joint is descibed as ecommended by the intenational society of biomechanics Figue : An oveview of the calculation of the knee angle fom the two IMUs at the tigh and shank. The pocedue can be divided into thee main steps: the alignment pocedue, the extended Kalman filte, and the knee angle calculation. Figue : Two inetial measuement units ae placed on the thigh and shank, which fom thei own local coodinate system. To compute the joint angle, the senso fames ae tansfomed in a mutual coodinate system, the joint coodinate system (JCS). in a mutual coodinate system, the so called joint coodinate system (JCS) as defined by Good and Sunday [9]. Fo each senso attachment the tansfomation fom the initial senso fames into the JCS and the esulting alignment of senso is done using the idea of the functional alignment pocedue of Fave et. al [7]. The joint motion is detemined by the oientation of each segment and is descibed in the XYZ-Eule angle epesentation. The otation matix that tansfoms the senso fame at any time step into the initial senso fame is defined by the multiplication of the single otation matices aound each

3 axis and is detemined by c c c s s R i = 4c s + s s c c c s s s s c 5 () s s c s c s c + c s s c c whee c and s denotes the cos and sin function and,, and ae the otation angles about the U, V, and W axes, espectively [4].. Alignment of Senso Fames The alignment pocedue is divided into two steps. The senso fames of the thigh and shank ae fist aligned vetically with the JCS (Z-axis alignment). Then, the senso fame of the shank is otated aound the Z-axis to be aligned hoizontally with the senso fame of the thigh (XYotation). Fo the vetical alignment, the inetial data of the acceleomete fom the motion still standing is equied, whee the subject stands still with staight legs fo ten seconds. As the gavity is pominent in the signal of acceleometes duing static conditions [4], the aveaged gavitational vecto g is detected fo each senso fame. It is used to calculate the otation matices R Z and R Z, which align the vetical components W and w, espectively, with the vetical axis of the JCS, Z. Z is defined by (,, ) T. Each otation matix is computed by [] kxkxv + c R Z = 4k xk yv + k zs kxkyv kzs k yk yv + c kxkzv + kys k yk zv k xs 5 k xk zv k ys k yk zv + k xs k zk zv + c whee is the misalignment angle between g and (,, ) T and k the otation axis, which is the thee-dimensional pependicula unit vecto to g and (,, ) T. The abbeviations s and c symbolize the sin and cos functions, and v = cos( ). Fo the hoizontal alignment the motion AA-otation as defined by Fave et. al [5], is equied. The staight leg is lifted up and down lateally fo seconds, which poduces an appoximately constantly oientated angula ate vecto in the senso fame of thigh and shank. The misalignment angle of the detected angula ate vectos! and! in the senso fame of thigh and shank ae used to fom the otation matix R XY, which otates the senso fame of the shank aound the aleady aligned Z-axis to align it with the senso fame of the thigh. Fo each time step k,! and! ae pojected on the UV- and uv-plane, espectively. The misalignment angle k of the pojected angula ate vectos is fist calculated fo each time step by the cosine function and then aveaged with the weighting function accoding to Fave et. al [5] by P N k= = (~! k,x~! k,y) T k P N k= ~! k. () N is the amount of time steps. is the weighted aveaged misalignment angle and is used to compute the otation matix R XY by cos( ) sin( ) R XY = 4sin( ) cos( ) 5. (). Extended Kalman Filte Two similaly designed standad EKF ae used to descibe the oll and pitch oientation of the two adjacent segments. The EKF is designed with an eight-ow state vecto as ~a ~x = B~! A, (4) containing the thee-dimensional acceleation ~a of the acceleomete, the thee-dimensional angula ates ~! of the gyoscope, both expessed in the thee axes of the senso fame, and the oll and pitch oientation angles. The otation between the initial fame and the senso fame at a time step k is defined by the thee Eule angles, and. Fo the calculation of the flexion/extension knee angle only the components oll and pitch ae needed. The dynamic system f is modeled linealy as 8 f : ~a k = ~a k + ~u a k >< f 4 6 : ~w k = ~w k + ~u w k f = (5) f 7 : k = k + t >: k f 8 : k = k + t k, whee k indicates the time step, t denotes the time inteval between each time step, ~u a and ~u w ae the vectos of noise on acceleation and angula ates, and and denote the time deivatives of and. Angles ae calculated fom the angula ates using the Eule fomulation. In evaluations of the pesented knee angle algoithm, it was seen that the yaw component of the gyoscope angula ate vecto is the main eason fo difts in the outputs of the EKF. Theefoe, in the calculation of oientation angles the assumption is made that the gyoscope yaw axis is zeo. Setting! =, f 7 and f 8 ae estimated by f 7 : = k + t [! +tan( )! sin( )] (6) f 8 : = k + t [! cos( )]. (7) The obsevations of the dynamic system ae the theedimensional acceleation of the acceleomete and the theedimensional angula ates of the gyoscope, which ae both measued in the senso fames of thigh and shank. The measuement is descibed by ~ hk = ~ak ~! k + ~ b + ~v k, (8) whee ~v is the measuement noise. The output of the gyoscope is defined by the angula ate vecto ~! and by the bias ~ b, which is assumed to be constant fo each tial and is detemined fo each axis to be the aveage value of angula ates ove the time steps of each tial. This assumption is based on the cyclical behavio of movements. The measuement and pocess noise covaiance matices ae defined by a u Id Q = 4! u Id 5. (9) and! u, and ae pa- Id denotes the identity matix and u, a ametes of the algoithm. R = Id 6 6. ()

4 .4 Flexion/extension Knee Angle Calculation The flexion/extension knee angle is defined in the sagittal plane of the leg and is the intesection angle of the vetical component of the senso fame of thigh and shank. The elative oientation of segments ove time is estimated by the EKF, whee the oientation is based on the initial senso fame. To calculate the tansfomation matix of each senso fame at any time step into the initial senso fame, R i, as detemined in equation (), is used. The vetical component of the senso fames fo each time step expessed in the initial senso fames is then calculated using the oll and pitch component estimated by the EKF by i k = R sin( k) A sin( k) cos( k) A () cos( k) cos( k) fo the thigh and i k = R sin( k) A sin( k) cos( k) A, () cos( k) cos( k) fo the shank. The vetical component expessed in the initial senso fames can futhe be tansfomed in the JCS using the vetical and hoizontal alignment matices R Z, R Z, and R XY. Descibing the whole tansfomation, the vetical component of the senso fames at any time step can be descibed with and based on the JCS as k = R Z R i k () k = R XY R Z R i k (4) The flexion/extension knee angle fo each time step is calculated by pojecting and fo each time step on the X-Y-plane and detemining the intesection angle by knee = s accos z,k z,k z,k z,k C A, (5) whee s =sign( z,k z,k ) defines the sign of otation and denotes the dot poduct. The estimated flexion/extension knee angle knee is the final esult of the pesented joint angle calculation method.. EXPERIMENTAL VALIDATION. Inetial Measuement System Fo evaluating the pesented algoithm, two inetial measuement units (IMU) (Invensense, Sunnyvale, CA, USA) containing an acceleomete (± 6 g) and a gyoscope (± /s) wee attached to the thigh and the shank of the ight leg. Double-adhesive tape was used to attach the sensos to the skin o tight touses, causing a easonable fim attachment to the segments. The position of the measuement units was selected with poximity to bones to minimize atifacts though muscle movements. A data logge was attached on the thigh and allowed ecoding inetial data fom both sensos on a SD-cad at Hz. Figue shows the exact positioning of sensos. Figue : Attachment of the IMUs (top and middle box) and the data logge (bottom box) duing data collection. The IMU of the shank was positioned fou centimetes unde the tochante majo, while the IMU of the thigh was positioned fou centimetes unde the middle of the fontal tibia. Fo the efeence system, eflective makes wee attached to the leg.. Measuement System The gold standad in motion analysis is the usage of an camea motion tacking system, which tacks eflective makes ove time. Theefoe, as efeence to the inetial-based knee angle, a camea motion tacking system with eight camaas was used (Qualysis, Götebog, Sweden). The efeence knee angle was calculated using Visual -D Reade (C-Motion, Gemantown, Mayland, USA) at Hz. The attachment of eflective makes can be seen in Figue. The camea system and the inetial senso ecode wee synchonized by a wieless tigge system with high accuacy and low jitte []. Any emaining systematic time o set between the two systems was emoved befoe pefoming the evaluation.. Study Design The study was conducted at the Motion Lab of the FAU Elangen-Nuembeg and was appoved by the local ethics committee. Infomed consent was obtained fom the test subjects. In total, seven subjects paticipated in the study. Thei anthopometic data is pesented in Table. The study contained seven motions. Fo the vetical alignment of sensos the subject stood still fo ten seconds. The AAotation, whee the ight leg is lifted up and down lateally, was used fo the hoizontal alignment of sensos. The additional motions wee walking, jogging, unning, squats, and countemovement jumps. These five dynamic motions diffe in speed and magnitude of the change of the knee angle and wee used to evaluate the knee angle calculation algoithm duing dynamics. All motions wee pefomed on a two-belt teadmill to simplify execution. Some data had to

5 Anthopometic data geneal Numbe of Subjects 7 Female 4 Male Age (yea) 5 ± Height (cm) 78 ± Weight (kg) 75 ± 4 Table : The anthopometic data of the test subjects (mean ± standad deviation). Numbe of test data Still Standing 7 AA-Rotation 7 Walking. m/s 7 Jogging. m/s 7 Running. m/s 5 Squats 6 Jumps 6 Table : Numbe of test data used fo the evaluation of each dynamic motion. The test data includes the inetial data of acceleomete and gyoscope attached on the thigh and shank EKF Output and Calculated Knee Angle knee angle oll thigh oll shank pitch thigh pitch shank Figue 4: Flexion/extension knee angle calculated using the outputs of the EKF oll and pitch of thigh and shank duing walking at. m/s. Dynamic motion RMSE in Coelation mean ± std mean ± std Walking. m/s 7. ± ±. Jogging. m/s 7. ± ±. Running. m/s. ± ±.5 Squats 9.7 ±..976 ±.6 Jumps 7. ±.9.99 ±.6 Table : Aveage and standad deviation of RMSE and Peason-coelation fo dynamic motions. be excluded due to missing o incomplete senso data. The numbe of test data used fo evaluation fo each motion is listed in Table..4 Evaluation of the Knee Angle The inetial senso based estimated flexion/extension knee angle was evaluated on all five dynamic motions in compaison to the camea motion tacking system. The paametes a! u, u, and wee detemined systematically in compaing the esulting knee angle of di eent paamete combinations fo a single subject. The optimal paamete combination was chosen to have the highest Peason-coelation of the esulting knee angle in compaison to the camea system as efeence. The oot mean squaed eo (RMSE) and the Peasoncoelation was then computed fo ten seconds. To emove any systematic amplitude o set between both systems, the knee angle outputs wee aligned befoe the evaluation was pefomed. In ode to compae the pefomance of the pesented knee angle calculation algoithm, the of the two systems wee aligned befoe paamete computation. This amplitude shift was calculated by aveaging the position of minima in the angle data and calculating the aveage o set between inetial and efeence system. Theeby, a systematical o set, which could be caused by impefect attachment of the sensos, is not consideed in the evaluation. 4. RESULTS Figue 4 illustates the knee angle calculation using the outputs of the EKF fo the data set walking with. m/s. The paamete seach esulted in u a! =, u =, and =. The esults of the evaluation of all subjects ae shown in Table, whee the RMSE and Peasoncoelation ae aveaged ove the esults of numbe of available test data. The mean RMSE and mean Peason-coelation, both aveaged ove the aveage of the dynamic motions wee 8. and.97 with a mean standad deviation of.4 and., espectively. In Figue 5, the knee angles estimated fom the inetial measuement system and the camea system ae compaed fo one subject pefoming the di eent motions. 5. DISCUSSION This study demonstated an algoithm to compute the knee flexion-extension angle fom two body-won inetial sensos. The extended Kalman filte, which is often used in the liteatue fo human motion analysis [8] was adapted to highly dynamic motions and combined with a functional alignment pocedue [5] fo aligning senso fames without the need of an extenal camea system. Duing the validation the inetial-based knee angles was estimated ove a second peiod with an mean RMSE and mean Peason-coelation of 8. ±.4 and.97 ±.. This shows that the pesented algoithm allows to obtain su ciently accuate knee angle estimates fom body-won inetial sensos, even duing high dynamic motions. The estimated knee angles coelated with a high accuacy, even fo the highly dynamic jumps. This means that the detection of fast changes that ae small is achieved pecisely. Regading the accuacy of the knee angle estimation and the usage of the inetial-based estimation pocedue in spots, the pesented algoithm cannot be used as a tool in compaing motion patten of di eent athletes to each othe o a camea efeence system, as the accuacy is to low. Futhe impovement egading the constancy fo di eent speed is compulsoy. As the eo of the estimated knee angle to the efeence system stays acceptably constant ove each speed the pesented knee angle estimation tool could be used to analyse and optimize the motion patten of one athlete individually fo one selected speed. Moeove, the pesented

6 Walking with. m/s Jogging with. m/s 4 5 Runnig with m/s Squats Countemovement Jumps Figue 5: Knee angles computed by the algoithm compaed to the camea efeence knee angles fom the camea system fo one subject pefoming all five dynamic movements. Additionally the knee angle estimation eo is shown. knee angle estimation tool could still be used to tack aveage values of the biomechanics of the motion ove time. Othe eseache have investigated the inetial-based knee angle calculation duing elatively slow motions [], [], [7], Coope et. al [] evaluated thei wok on unning with. m/s with a RMSE of.4, which is bette than the pesented algoithm. Howeve, in contast to the algoithm pesented in this pape, Coope based the alignment of senso fames on a camea system. This impoved the esulting knee angle, but is citical egading the usage of inetial measuement units in a eal envionment in the field of spots. In contast, the pesented algoithm elies on the functional alignment pocedue pesented by Fave et. al [5]. This allows the estimation of the joint angle without any initialization fom a efeence system. Most ambulatoy thee-dimensional oientation measuement systems include acceleometes, gyoscopes, and magnetometes [8], [7]. Howeve, none of these studies epoted on the eo of the detemination of the knee angle duing dynamic motions. Fave et. al [5] calculated the flexion/extension angle based on epeated alignment motions tials with an eo less then. Howeve, thei esults wee only based on slow walking and was not evaluated on high dynamic motions. As the paametes of the pesented algoithm wee optimized fo dynamic motions, the pesented algoithm could not achieve such a high accuacy duing walking. Howeve, the accuacy was quite stable even duing highly dynamic motions, e.g. jumping. A futhe optimization of the algoithm paametes to the motion task will be subject of futue wok. While the pesented algoithm had a vey high coelation fo all motions, it could not achieve an RMSE eo below 7, which is highe than eos epoted by othe appoaches. Howeve, the accuacy of the pesented algoithm is su cient fo many tasks and applications, e.g. feedback taining o pefomance evaluation. Due to the high coelation, the eo is most pobably caused by systematic o sets o by dift. Duing the evaluation it was also found that the accuacy deceased with inceasing speed. Again, the main eason might the inceasing dift and inaccuacy of the gyoscope when measuing lage angula ates. Futhemoe, stonge vibation of muscles can poduce additional noise in sensos and distot the attachment of sensos on the leg. Both poblems could be solved by incopoating a bias tem in the EKF. Additionally one could incopoate pio knowledge about the motion. This could be used to detect steps and to eset the angle calculation afte each stide. One impotant limitation of the pesented wok is the stability of the EKF in the tials with highly dynamic motions. Duing the expeiments the EKF was found as stable, but the stability is still dependent on the chosen paametes and dynamics. This means that the estimation of knee angles in even highe dynamic motions, as duing socce could poduce instabilities. Then the paamete of the EKF would have to be adopted to the dynamic motion and an automatic adjustment of the paametes might become necessay. This will be investigated in futue wok. To ou knowledge, this is the fist study pesenting and evaluating the estimation of knee joint angles fom inetialsensos with the pupose of the usage in dynamic spots. We believe it is a futhe step towads the usage of inetial-based motion analysis duing spot applications. 6. SUMMARY This pape pesented an inetial senso based knee angle calculation algoithm usable in the novel application field of unning spots. Knee angles ae estimated with an extended Kalman filte using the data of acceleomete and gyoscope both attached on the thigh and shank. The calibation of sensos is done without the usage of an extenal system. The pape pesented an impotant step towads the application of inetial-sensos fo analysis of joint angles in spots. Using the algoithms pesented in this pape, objective feedback of motions can be obtained fom the inetial sensos. This could constantly help impoving the pefomance of the athlete in taining o even in competitions. 7. ACKNOWLEDGMENTS We thank all paticipants of this study. This wok was suppoted by the Embedded Systems Institute (ESI) Elangen, the Bavaian Ministy fo Economic A ais, Infastuctue, Tanspot and Technology and the Euopean Fund fo Regional Development. Additional suppot was povided by the adidas AG, Hezogenauach, Gemany. 8. REFERENCES [] J. Chadonnens, J. Fave, G. Gemion, and K. Aminian. A New Method fo Unconstained Measuement of Knee Joint Angle and Timing in

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