Accelerometer and rate gyroscope measurement of kinematics: an inexpensive alternative to optical motion analysis systems

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1 Journal of Biomechanic 35 (22) Short communication Accelerometer and rate gyrocope meaurement of kinematic: an inexpenive alternative to optical motion analyi ytem Ruth E. Mayagoitia a, *, Anand V. Nene b, Peter H. Veltink c a Sport, Health and Exercie, Staffordhire Univerity, Leek Road, Stoke on Trent ST4 2DF, UK b Roeingh Reearch and Development, Roeingh Rehabilitation Intitute, Enchede, The Netherland c Biomedical Technology Intitute, Univerity of Twente, Enchede, The Netherland Accepted 28 November 21 Abtract A general-purpoe ytem to obtain the kinematic of gait in the agittal plane baed on body-mounted enor wa developed. It conited of four uniaxial eimic accelerometer and one rate gyrocope per body egment. Tet were done with 1 young healthy volunteer, walking at five different peed on a treadmill. In order to tudy the ytem accuracy, meaurement were made with an optic, paive-marker ytem and the body-mounted ytem, imultaneouly. In all the comparion cae, the curve obtained from the two ytem were very cloe, howing root mean quare error repreenting o7% full range in 75% of the cae (overall mean 6.64%, tandard deviation 4.13%) and high coefficient of multiple correlation in 1% of cae (overall mean.9812, tandard deviation.2). Calibration of the body-mounted ytem i done againt gravity. The body-mounted enor do not hinder natural movement. The calculation algorithm are computationally demanding and only are applicable off-line. The body-mounted enor are accurate, inexpenive and portable and allow long-term recording in clinical, port and ergonomic etting. r 22 Elevier Science Ltd. All right reerved. Keyword: Accelerometer; Gyrocope; Gait kinematic; Portable gait analyi; Knee moment 1. Introduction Optical motion analyi ytem are often ued in the tudy of human movement. However, thee ytem are expenive, only allow meaurement in a retricted volume, and the marker are eaily obcured from viion reulting in incomplete data. More recently, body-mounted enor have alo been ued to obtain kinematic value (Bumann et al., 1995; Bogert van den et al., 1996; Dai et al., 1996; Luinge et al., 1999; Tong and Granat, 1999; Veltinket al., 1996; Veltink, 1999). A fully portable ytem can be obtained if a portable data logger i ued to gather the data from body-mounted enor. The ytem preented in thi paper i general-purpoe, combining accelerometer and rate gyrocope, able to deliver the following kinematic parameter in the *Correponding author. Tel.: ; fax: addre: rem2@taff.ac.uk(r.e. Mayagoitia). agittal plane: hankangle, thigh angle, knee angle, hankangular velocity, thigh angular velocity, knee linear acceleration, hankangular acceleration and thigh angular acceleration. To verify the accuracy of the bodymounted enor ytem, optical data were gathered imultaneouly uing a Vicon Sytem. Only the parameter of hankangle, hankangular velocity, knee linear acceleration and hank angular acceleration are preented in thi paper a repreentative example. 2. Material and method 2.1. Model decription In the two-dimenional (agittal plane) model, the hankand foot were conidered a a ingle egment referred to a hank. Shank and thigh were repreented by two rigid egment k and k þ 1 connected by a imple hinge knee joint (Fig. 1) /2/$ - ee front matter r 22 Elevier Science Ltd. All right reerved. PII: S (1)231-7

2 538 R.E. Mayagoitia et al. / Journal of Biomechanic 35 (22) Accelerometer ignal Calculation of linear acceleration The accelerometer ignal ~ k;i at any point i of a rigid body k can be expreed a a vector ~x ¼ð~x 1 ; ~x 2 ; ~x 3 Þ T on the bai of three independent ignal vector ~ k1 ;~ k2 ;~ k3 at poition ~r k1 ;~r k2 ;~r k3 (Veltinkand Boom, 1996) ~ ki ¼ X3 Segment 2 Thigh j¼1 y F hy, a hy z x Segment 1 Shank φ 2 F hx, a hx M 2, I 2 M1, I 1 ω 1, α 1 m 2 g Moh a c2y a c2x M ok -Fk 2x, -ak 2x -Fk 2y, -ak2y a c1y m 1 g φ 1 M ok a c1x ω 2, α 2 Fk 1y, ak 1y Fk 1x, ak 1x Fig. 1. Free body diagram of the thigh and hankegment during wing. ~x j ~ kj : ð1þ The coordinate of vector ~x can be etimated by application of Cramer Rule. The body-fixed acceleration ~a t k and ~ar k meaured by tangentially and radially oriented accelerometer at the reference point of the body-fixed frame can be repreented by ~ t k ¼ ~r k2 ~ t k1 ~r k1 ~ t k2 ~r k2 ~r k1 ; t k ¼ g in j k þ a t ; ð2þ ~ r k ¼ ~r k2 ~ r k1 ~r k1 ~ r k2 ~r k2 ~r k1 ; r k ¼ g co j k þ a r : ð3þ If the abolute egment angle j k i known, it i poible to determine the linear acceleration component a t and a r at thi reference point (Willemen et al., 1991). Eq. (2) i ued below to obtain the linear acceleration of the knee Calculation of angular acceleration Two accelerometer tangentially mounted on a rigid body k at point i and i þ 1 meaure the tangential acceleration component ~ t k;iþ1 and ~t k;i : Since g and ~t k; are independent of the poition along the egment, the quantity (~ t k;iþ1 ~t k;i ) i related directly to the angular acceleration:.~j k ¼ ~t k;iþ1 ~t k;i ~r k;iþ1 ~r k;i : ð4þ 2.3. Gyrocope ignal Calculation of angular velocity The angular velocity i meaured by a rate gyrocope through the Corioli force and can be found directly a ~o gy : ð5þ Calculation of angle In general, the orientation angle derived from the angular velocity ~o gy meaured by a rate gyrocope i given by (Bortz, 1971) Z ~j k ¼ ð~o gy A þ ~o off Þ dt þ ~j off ; ð6þ t where ~o gy i the gyrocope output ignal, A the proportionality factor, ~o off the angular velocity offet, and ~j off the initial integration offet (t ¼ ). The reference angle (integration offet needed by the rate gyrocope) can be obtained from two accelerometer mounted perpendicular to each other at poition i on body egment k (Fig. 2) under tatic condition with j off ¼ arctan ~t ki ~ r : ð7þ ki 2.4. Experimental intrumentation Four pair of uniaxial accelerometer (IC Senor P) were mounted on two aluminum trip, 3 cm long and 2 cm wide. The accelerometer meaured the tangential and radial acceleration at point i and i þ 1 of each egment (Fig. 2). A gyrocope (Murata ENC-5EB) wa attached to the midpoint of each aluminum trip to meaure the angular velocity. Data were recorded at 1 Hz. Calibration recording were made before and after data collection of each ubject. Firt the trip were placed in line with gravity for two recording when the radial accelerometer regitered +1g and 1g. Then the trip were placed perpendicular to gravity, to meaure +1g and 1g in the tangetial accelerometer. Dynamic calibration were made for the gyrocope putting the enor through motion of 91 and 181 in a known

3 R.E. Mayagoitia et al. / Journal of Biomechanic 35 (22) r a k+1,i ϕ k+1 a t k+1,i the left lateral maleolu, lateral condyle and greater trochanter. The ditance between the enor and the proximal joint marker were meaured with a meauring tape. The marker were tracked at 5 Hz Data analyi Segment 2 Thigh Segment 1 Shank a r k,i+1 time. The alignment were aited by a carpenter quare and a bubble level. For further detail on accelerometer calibration, ee Veltinket al. (1998) Tet protocol a t k,i+1 ω k+1 a r k+1,i+1 a r k,i a t k+1,i+1 Subject were 1 normal male aged between 23 and 27 year, who had given informed conent. The volunteer performed ten 1 or 12 treadmill walking trial coniting of two repetition at five peed (very low=1.4 km/h, low=2.1 km/h, average=2.7 km/h, fat=3.6 km/h and very fat=4.6 km/h) wearing their uual hoe. In addition, two trial of quiet tanding before and after each eion were recorded. The aluminum trip with the enor wa placed on the frontal, medial apect of the hankand thigh of the ubject and attached nuggly with wide, elaticized velcro trap. It wa expected that vibration of the metal trip during walking would be minimal and that direct impact of the enor would be very remote. Data from the body-mounted ytem and from a Vicon motion-meaurement ytem were recorded imultaneouly. Reflective marker were placed over ω k -ϕ k a t k,i Fig. 2. Accelerometer and rate gyrocope placement on the lower limb. P i, Matlab wa ued for all ignal proceing. A ixthorder Butterworth low-pa filter with a cut-off frequency of 3 Hz wa ued to remove noie from all the raw data. Only the agittal plane component of the recorded marker poition were ued. The coordinate of ankle, knee and hip were ued to find the diplacement of the knee joint and the angular diplacement of the hank. By numerical differentiation, the repective velocitie were found. A econd differentiation yielded the acceleration. The enor data were decimated to 5 Hz to make the data directly comparable. For the comparion between the enor and Vicon reult, the root of the mean of the quared difference (Eq. (8)) wa ued to compare the cloene in amplitude. Vicon reult were ued a reference rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X T RMS ¼ T ðj i¼1 krðiþ j k ðiþþ 2 : ð8þ The ubcript r indicate a reference meaure. The angle meaurement j k i ued a an example. A percent error wa calculated a the ratio between the RMS error to the average peak-to-peak amplitude of the marker data (Table 1). The coefficient of multiple correlation (Kadaba et al., 1989) wa ued to lookat the cloene in the hape of the two ignal. In thi cae, the mean of the two ignal being compared i ued a reference vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P N P u T j¼1 i¼1 CMC ¼ t 1 ðy jt %Y t Þ 2 =TðN 1Þ P T i¼1 ðy jt %YÞ 2 ; ð9þ =ðnt 1Þ P N j¼1 where T i the number of ample and N i 2, the number of compared ignal. 3. Reult 3.1. Meaurement ytem verification The number of cae (out of 2) in each comparion i indicated in Table 2, together with the RMS and CMC reult. Miing cae are due to data lot to file archiving problem or to one or more of the marker being lot from viion. Fig. 3 how example of graph of the four comparion. In three of the four comparion, the RMS error are o7% of the full range of the meaurement and the found CMC are above.98. However, for the linear acceleration of the knee (comparion number 3), the

4 54 R.E. Mayagoitia et al. / Journal of Biomechanic 35 (22) Table 1 Percent error of the kinematic meaurement. Ratio of RMS error to average peakto peakvalue obtained from our own optical marker reult 1. Shankangle 2. Shankangular velocity 3. Knee linear acceleration 4. Shankangular acceleleration Gyrocope v. Vicon Gyrocope v. Vicon Accelerometer v. Vicon Accelerometer v. Vicon RMS (rad) RMS (rad/) RMS (m//) RMS (rad//) Very low Mean Ref % error Slow Mean Ref % error Intermediate Mean Ref % error Fat Mean Ref % error Very fat Mean Ref % error Percentage error of RMS (mean) to Vicon full range (ref) (Ref=peak-to-peak value averaged). Table 2 Reult of comparing kinematic meaurement obtained by body-mounted enor and optical marker (1) Shankangle (2) Shankangular velocity (3) Knee linear acceleration (4) Shankangular acceleration Gyrocope v. Vicon Gyrocope v. Vicon Accelerometer v. Vicon Accelerometer v. Vicon RMS (rad) CMC RMS (rad/) CMC RMS (m//) CMC RMS (rad//) CMC Very low Mean Stdev Cae Slow Mean Stdev Cae Intermediate Mean Stdev Cae Fat Mean Stdev Cae Very fat Mean Stdev Cae

5 R.E. Mayagoitia et al. / Journal of Biomechanic 35 (22) Abolute Shank Angle by Gyrocope and Vicon 3 Shank Angular Velocity by Gyrocope and Vicon.6 2 Radian (a) Radian/econd (b) Linear Acceleration of the Knee by Accelerometer and Vicon 8 Shank Angular Acceleration by Accelerometer and Vicon m// 2 Rad// (c) -4-3 (d) Fig. 3. Repreentative graph to illutrate comparion a d; ubject number 7, intermediate velocity. ViconFolid line. SenorFdahed line. error are between 11% and 15% and CMC drop to.93. The algorithm to calculate the linear acceleration of the knee from accelerometer data depend on the ditance between the proximal tangential accelerometer on thigh and hankand the knee joint. Slippage of the trip on which the enor were mounted would give a rie to a change in the actual ditance between the enor, and thi could account for the mall, over etimation. The ditance between the enor and the knee wa only meaured at the beginning of the eion. 4. Dicuion 4.1. Accuracy of kinematic meaurement The body-mounted enor give reult that are very cloe to thoe of Vicon preenting mall RMS and large CMC value. Error do increae at the highet peed for the accelerometer data, which for everal ubject uffered from deformed peak, probably due to the enor being hit or vibrated during heel trike. Thi hould be taken into account when deigning future application involving accelerometer. The rate gyrocope were not affected in thi way Contribution of thi tudy and future work In thi tudy, a treadmill wa ued within the viion cube of the Vicon ytem in order to record everal conecutive tep. There are ubject for whom it would not be afe to ue a treadmill. However, the bodymounted enor combined with a portable data-logger contitute a fully portable ytem that can be ued for a many conecutive tep a deired in almot any environment. The body-mounted enor ytem ubject of thi paper ha been applied in a biomechanic tudy (Nene et al., 1999). A imilar ytem could alo be ued in port ituation with acceleration comparable to thoe of walking. The method for finding kinematic by uing bodymounted accelerometer and rate gyrocope i accurate a compared to a Vicon ytem, for different normal ubject and at five different walking peed. The ytem

6 542 R.E. Mayagoitia et al. / Journal of Biomechanic 35 (22) baed on body-mounted enor i inexpenive. The metal trip where the enor are mounted i more cumberome than the marker but doe not alter movement. Acknowledgement We are grateful to the STW, Dutch Technology Foundation, for the funding for thi project; to Andrea Heyn and Eric Camiro for their valuable aitance. Reference Bogert van den, A.J., Read, L., Nigg, B.M., A method for invere dynamic analyi uing accelerometry. Journal of Biomechanic 29, Bortz, J.E., A new mathematical formulation for trapdown inertial navigation. IEEE Tranaction on Aeropace and Electronic Sytem 7, Bumann, J.B.J., Veltink, P.H., Koelma, F., van Lummel, R.C., Stam, H.J., Ambulatory monitoring of mobility-related activitie: the initial phae of the development of an activity monitor. European Journal of Phyical and Medical Rehabilitation 5, 2 7. Dai, R., Stein, R.B., Andrew, B.J., Jame, K.B., Wieler, M., Application of tilt enor in functional electrical timulation. IEEE Tranaction on Rehabilitation Engineering 4, Kadaba, M.P., Ramakrihnan, M.E., Gainey, W.J., Gorton, G., Cochran, G.V.B., Reproducibility of kinematic, kinetic, and electromyographic data in normal adult gait. Journal of Orthopedic Reearch 7, Luinge, H.J., Veltink, P.H., Baten, C.T.M., Etimating orientation with gyrocope and accelerometer. Technology and Health Care 7, Nene, A., Mayagoitia, R.E., Veltink, P.H., Aement of rectu femori function during initial wing phae. Gait and Poture 9, 1 9. Tong, K., Granat, M.H., A practical gait analyi ytem uing gyrocope. Medical Engineering and Phyic 21, Veltink, P.H., Senory feedback in artificial control of human mobility. Technology and Health Care 7, Veltink, P.H., Boom, H.B.K., D movement analyi uing accelerometryftheoretical concept. In: Pedotti, A., Ferrarin, M., Quintern, J., Riener, R. (Ed.), NeuroprotheticFFrom Baic Reearch to Clinical Application. Springer, Berlin, pp Veltink, P.H., Bumann, H.B.J., Vrie de, W., Marten, W.L.J., Lummel van, R.C., Detection of tatic and dynamic activitie uing uniaxial accelerometer. IEEE Tranaction on Rehabilitation Engineering 4, Veltink, P.H., L.otter, J.C., Schipper, J., Olthui, W., Bergveld, P., Procedure for in-ue calibration of triaxial accelerometer in medical application. Senor and Actuator A 68, Willemen, A.T.M., Frigo, C., Boom, H.B.K., Lower extremity angle meaurement with accelerometerferror and enitivity analyi. IEEE Tranaction on Biomedical Engineering 12,