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Applied Soft Computing 11 (2011) 4757–4765

Contents lists available at ScienceDirect

Applied Soft Computing

j ourna l ho mepage: www.elsev ier .com/ locate /asoc

NFIS based knee angle prediction: An approach to design speed adaptive contraateral controlled AK prosthesis

eepak Joshi ∗, A. Mishra, Sneh Anandenter for Biomedical Engineering, IIT Delhi 110016, India

r t i c l e i n f o

rticle history:eceived 21 June 2010eceived in revised form 11 April 2011ccepted 17 July 2011vailable online 23 July 2011

a b s t r a c t

Prediction of prosthetic knee joint angle plays a crucial role in performance of above knee (AK) prosthesis,as it helps in estimating intended posture and movement of amputee. This paper applies a first-orderSugeno type ANFIS (Adaptive Neuro-Fuzzy Inference System) to predict the knee angle from contra lateralknee angle with different walking speed. The other two variables to train ANFIS were derivative of kneeangle trajectory and the best fit curve equation between the trajectories of both knee angles. The average

eywords:NFISontra lateralpeed adaptiveK prosthesis

RMSE was 3.4 ± 1.4◦ with wide range of walking speeds, using few Fuzzy rules. This research work hasdirect application in the design of a contra lateral controlled speed adaptive AK prosthesis.

© 2011 Elsevier B.V. All rights reserved.

nee angle

. Introduction

The angular velocity command for prosthetic knee joint ensureshe movement to a desired position with a joint output stiffness, tochieve real time speed adaptation. Concern arises as multiple bodyounted sensors are used, creating unwieldy feel for the patient,hich may affect the prediction results [1]. The challenge is reduce

he number of mounted sensors and yet to achieve desired pre-iction accuracy. Electromyogram (EMG) from the residual partf the lower limb has been extensively used for control the pros-hetic knee joint. Most EMG based prosthetics relies on gait modeecognition for locking mechanics of prosthetic knee joint [2–7].a et al. used EMG for the angular velocity control of prostheticnee joint for volitional controlled activities [8]. Donath [9] con-luded that use of EMG during gait would be challenging as reliableMG acquisition will be much challenging in presence of noiseick up and movement artifacts. Further EMG does not give direct

nformation of posture as the joint angle. EMG and knee angle oformal limb was used to predict the knee angle of a prosthetic

imb using Radial Basis Function Neural Network (RBFNN) [10];erformance degrades by sweating especially in tropical regions.his enhances fatigue due to increased effort in locomotion. Hence

chieving higher accuracy requires the use of numerous electrodesnd complex signal processing. In contrast, knee angle measure-ent is not affected by physiological parameters and can overcome

∗ Corresponding author.E-mail address: joshideepak2004@yahoo.co.in (D. Joshi).

568-4946/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.asoc.2011.07.007

the problems. Attempt was made [11] to predict the knee anglefrom the normal limb knee angle was performed using Neural Net-work and an Adaptive Neural Controller. The inputs to the networkwere first and second order derivatives of the knee angle. It showedbetter performance than a Linear Quadratic Regulator (LQR) con-troller with limited range of knee angle and constant speed. Alteringgait speed has significant effect on lower limb kinematics. Further,speed ranges differ among healthy population and patients havingstroke and neuromuscular disease. The knee joint kinematics waschanged by 0–10◦ with walking speed variation of 0.5 m/s. [12].Lelas et al. observed the reduction in gait speed from 2 to 1 m/sleads to an average absolute change of 4.5◦ in peak sagittal angles[13]. Five lower limb angles viz. knee, ankle, thigh, shank and footwere predicted with significant correlations between angles andspeed [14]. An algorithm which can predict the knee angle for widerange of walking speeds with a high accuracy needs to be incor-porated. Correlation between the speed and contact time of stancephase and the peak flexion angle in swing phase was used to controlthe damping factor with varying speed for designing speed adap-tive prosthesis [15]. Present work uses only knee angle to predictthe prosthetic knee joint for a wide range of walking speed.

A Multi Layer Perceptron (MLP) using back propagation andRBFNN has been used earlier using the history of knee joint angleand ground reaction force (GRF), to predict the knee angle [16].Investigators have used Proportional Derivative (PD) feedback and

plant model along with the Neural Network to predict knee angle[17]. Soft computing tools like Neural Network and fuzzy logic learnfrom the available dataset and hence avoid the need of plant model-ing. Using neural network approach, the acceleration and angular

4758 D. Joshi et al. / Applied Soft Computing 11 (2011) 4757–4765

Fig. 1. (a) Gait lab with cameras location Fig. 1. (b) Markers in walking trial.

ollect

vpmato2aoaFe

Fig. 2. Data c

elocity of foot and shank, in all three dimensions, were used toredict knee angle using Generalized Auxiliary Similarity Infor-ation (GASI) with Regression Neural Network. It introduced the

lgorithm for knee angle prediction with speed variation. Thoughhe lower and higher side of normal speed was restricted to ±10%f normal speed, the accuracy found was quite good; however,4 input variables were used for prediction [18]. ANFIS takes thedvantage of learning in Neural Network and uncertainty immunityf Fuzzy Logic. It applies a combination of the least-squares method

nd the back propagation gradient descent method for traininguzzy Inference System (FIS) membership function parameters tomulate a given training set. In the past ANFIS has been used in

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Fig. 3. Division of gait cycle into four phases.

ion protocol.

the modeling of a wire for Electrical Discharge Machining (EDM) aswell as in the function approximation of Pneumatic Artificial Mus-cle Force [19–21]. Present thesis used ANFIS to obtain the minimumnumber of rules to predict the knee angle of prosthesis side withwide range of walking speed. The only measurement is the kneeangle in sagittal plane while the other two inputs are derived fromcomputation of the knee angle.

2. Materials and methods

2.1. Subjects

Sixteen healthy adult male volunteers between 22 and 27 years

of age with no obvious and documented neurological or muscu-loskeletal deficiencies participated in this study. All participantsprovided written informed consent prior to testing.

Fig. 4. Derivative of all the four phases for a complete gait cycle.

D. Joshi et al. / Applied Soft Computing 11 (2011) 4757–4765 4759

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Fig. 5. Curve fitting for all the gait phase.

Fig. 6. A typical three input first-order Sugeno type ANFIS.

4760 D. Joshi et al. / Applied Soft Computing 11 (2011) 4757–4765

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Table 1ANFIS parameters and their values.

ANFIS parameter type Value

MF type Triangular functionNumber of MFs 8Number of nodes 136Number of linear parameters 32Number of non linear parameters 72Total number of parameters 104Number of Training data pairs 810Number of checking data pairs 393Number of fuzzy rules 32

0 1 2 3 4 5 6 7 81.5

2

2.5

3

3.5

4

4.5

5

#Subject

RM

SE

(Deg

ree)

Fig. 7. Triangular membership function.

.2. Data collection

Data was collected in a 3D motion analysis system using six CCDiRes cameras from Expert Vision Systems of M/s (Motion Anal-sis Corporation, Santa Rosa, CA, USA) as illustrated in Fig. 1(a).

set of twenty five Cleveland Clinic (Cleveland, OH, USA) retro-eflective surface markers were placed on the subjects to acquirehe joint angles during dynamic trials. For this study only kneeoints are considered for which the markers were placed as perhe trials requirement. Two markers to define knee centre and axisf rotation were placed along the flexion/extension axis of rotationt lateral and medial femoral condyle, during static trial. The staticrial was done for anthropometric calibration: one for the left andne for the right leg. Three markers were placed on the lower thighelow the mid point and three on the lower shank below the midoint shown in Fig. 1(b) for walking trials. It was done to ensurehe least amount of skin and muscle movement. In order to facil-tate unrestricted motion of the subject during walking, the static

arkers were removed for the walking trials. Walking trials wereollowed by static trials; however, the order does not matter forny inaccuracy in data collection.

The subjects were asked to become accustomed with walkingn the laboratory at their normal speed. They were further askedo walk with varying speeds. All this training data was collectedrom the Ergonomics Lab, Defense Institute of Physiology and Alliedciences (DIPAS), New Delhi. Data recording began 2–3 min afterhe subjects began walking. This was done to adapt the subjectsith the walk pathway. Fig. 2 is the schematic for experimental

rotocol. Seven to eight trials were performed for each locomotiveask to get repetitive data for comparison and analysis. The data

0 50 100 150 200 250 300 350 400 450 500

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Epochs

RM

SE

(Roo

t Mea

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quar

ed E

rror

)

Error Curves

training datachecking data

Number of epochs for Model Validation

Fig. 8. Error profile for training and checking data.

Fig. 9. RMSE for seven subjects.

was analyzed offline in order to develop the ANFIS algorithm. Thecorresponding data was used to train and test the network.

Data was collected at sampling frequency of 120 Hz. The datawas recorded for 3 s during each trial to ensure at least a completegait cycle. Some of the trials were not included for analysis due toincomplete information because of drop-out of markers or exces-sive noise. Noise was eliminated from the gathered data using a lowpass Butterworth filter with 6.0 Hz cut off [reference]. Collectedtrials were then tracked using Eva7.0 software (Motion AnalysisCoorporation, Santa Rosa, CA, USA) and subsequently exported toOrthotrak 6.2 software (Motion Analysis Coorporation, Santa Rosa,CA, USA). The data from Orhtotrak was imported to Matlab 7.0 forfurther analysis. Out of 360 samples, the single gait cycle infor-mation was used one by one rather than together as the multiplecycles. This was done as the walking speed was observed within thegait cycles for a single trial. Most of the movement was observed inthe sagittal plane, hence only the corresponding data is consideredfor the study. Knee angle derivative was computed using first orderdifference. For a constant and uniform sampling rate if the walk-ing speed changes temporal values of knee angle and its derivativealso changes. Therefore data with various speeds was included in

training the ANFIS.

Table 2Mean and standard deviation taken from RMSE calculated from 7 subjects.

Statistical parameters Average RMSE (◦) CCC

Mean 3.4 0.93Standard deviation 1.6 0.04

D. Joshi et al. / Applied Soft Computing 11 (2011) 4757–4765 4761

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le. (b)

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Fig. 10. (a) ANFIS performance for complete gait cyc

.3. Methodology

The complete gait cycle was divided into four phases based onagnitude and derivative of the knee angle. Fig. 3 clearly reveals

he potential of derivative to discriminate all the four phases on theasis of magnitude and slope sign.

The division of the gait cycle has been a popular choice amongesearchers for analysis and prediction. To estimate the requiredorque for knee movement the best regression fit was applied onhe gait cycle [22]. Here the sign and magnitude of the deriva-ive has been taken as the criterion for division of gait cycle intohases. However it was also kept in mind that the phases shoulde detectable. Fig. 4 shows the slope of all the four phases for aypical walking speed and witness the variation on the sign and

agnitude of the derivative.

.4. Curve fitting

For all the phases the third order polynomial from curve fittingas computed, between the right knee and left knee trajectory.

he curve fit polynomial output was calculated for each knee anglerom contra lateral limb. Following are the third order polynomialsor curve fitting between phases using least square error criterion

hase 1 RKA=0.0077 ∗ (LKA)3−0.35 ∗ (LKA)2+7.5 ∗ (LKA) − 36

(1)

hase 2 RKA = 0.005 ∗ (LKA)3 − 0.69 ∗ (LKA)2 + 25 ∗ (LKA) − 190

(2)

hase 3 RKA=0.0005 ∗ (LKA)3+0.074 ∗ (LKA)2−2.8 ∗ (LKA) + 42

(3)

hase 4 RKA=0.0077 ∗ (LKA)3−0.35 ∗ (LKA)2 + 7.5 ∗ (LKA) − 36

(4)

LKA – Left Knee Angle RKA – Right Knee AngleThese equations were followed while training the ANFIS with

ifferent speed of gait data.

Lags

Cross correlation between ANFIS and actual output.

Fig. 5 shows the used curve fitting polynomial output for a typ-ical walking speed. This output, for different speed, was a featureas the ANFIS input. Though the curve fitting polynomial itself givesgood approximation to predict the knee angle, as the speed changesa unique polynomial does not exist

2.5. ANFIS

ANFIS is a class of adaptive networks that are functionally equiv-alent to fuzzy inference systems. ANFIS architecture representsboth Sugeno and Tsukamoto fuzzy models. Here it was first-ordersugeno type ANFIS used to train the data.

For a first-order Sugeno fuzzy model, Fig. 6, a common rule isgiven below

Rule 1 : If x is A1 and y is B1, then f 1 = p1 ∗ x + q1 ∗ y + r1 (5)

where the parameters defining A1 and B1 membership functionalong with p1, q1 and r1 modifiy during the training. The descriptionof each layer in ANFIS is as following

Layer 1 corresponds to the membership function for the crispinputs. The parameters in this layer are called Premise parameters.

The membership function (MF) at layer 1 was found to be bestas triangular membership function, given as following

triangle(x; a, b, c) =

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

o, x ≤ a

x − a

b − a, a ≤ x ≤ b

c − x

c − b, b ≤ x ≤ c

o, c ≤ x

(6)

where the parameters a, b and c, in Fig. 7, determine the coordi-nates of the three corners of the underlying triangular MF, provided,a < b < c. This was selected heuristically while training ANFIS.

Layer2 performs T-norm operation on the incoming inputs.There are several types of T-norm operators. Here AND T-normoperator is used, given by,

w = �A(x) ∗ �B(y) (7)

Layer 3 performs normalization operation on incoming signals,given as,

wi = wi

w1 + w2, i = 1, 2 (8)

where i is the number of nodes

4762 D. Joshi et al. / Applied Soft Computing 11 (2011) 4757–4765

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MF#1MF#2

Fig. 11. Membership function before and after training ANFIS.

D. Joshi et al. / Applied Soft Computing 11 (2011) 4757–4765 4763

ase 1

l

w

t

i

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2

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Fig. 12. Fuzzy rules: ph

Layer 4 performs the multiplication for input from layer 3 andayer 1, given by,

i ∗ fi = wi(pi ∗ x + qi ∗ y + ri) (9)

Parameters in this layer are referred to as consequent parame-ers

Layer 5 computes the overall output as the summation of allncoming signals, given by,

i

wi ∗ fi =∑

iwi ∗ fi˙iwi

As the number of inputs was less, grid partition was used inhe input space to design the initial FIS. Subtractive clustering wasvoided as the high dimensionality was not obvious here. Numberf epochs for training data was selected on the basis of validationata to avoid over training within the subjects. They varied whileraining for different speeds.

.6. Training

ANFIS applies a combination of the least-squares method andhe back propagation gradient descent method for training FIS

embership function parameters to emulate a given training dataet. More specifically, in the forward pass of the hybrid learninglgorithm, node outputs go forward until layer 4 and the conse-uent parameters are identified by the least-squares method. Inhe backward pass, the error signals propagate backward and theremise parameters are updated by gradient descent [23]. The dataollected at variable speed was used for training, checking and test-ng data. During training the ANFIS both the training and checkingata was presented to avoid model over fitting. The speeds to trainnd test the data were chosen randomly and there was no interfer-nce between both of them.

. Results

Root Mean Square Error (RMSE) was used as a performancendex to calculate the error for training checking and testing data,sing the following equation

MSE =n∑

(Am − Am)2

m−1

here Am and Am are the mth actual and estimated output, respec-ively, and n is the total number of samples to be presented.

to phase 4 (Clockwise).

Cross-correlation is a measure of similarity of two waveforms asa function of a time-lag applied to one of them and hence hasbeen used here to assess the performance of ANFIS. For discretefunctions, the cross-correlation is defined as:

(f ∗ g)[n] =+∞∑−∞

f [m] ∗ g[n + m]

where f and g are ANIFS output and actual output, having msamples each. The n variable corresponds to the lag (in num-ber of samples) by which the time series is shifted. The plotfor error in training and checking data for a typical selectedphase is shown in Fig. 8. The trained ANFIS, corresponding tothe epoch from where the over fitting starts, is used as the finalmodel for testing Fig. 8. Table 1 presents the feature of developedANFIS.

The average RMSE and standard deviation (SD) for seven sub-jects within random trials is shown in Fig. 9.

The overall average RMSE and SD for the subjects with alltested random speed was observed as mean = 3.4◦ SD = 1.4◦. Inother way the accuracy achieved is 95.2% of the maximum angleduring the complete gait cycle. Performance was also quantifiedusing maximum cross correlation coefficient (CCC) [25] betweenANFIS and actual output. The low and high 95% Confidence Inter-val (CI) for maximum CCC is 0.90 and 0.94. Table 2 presents thesummary.

For a subject’s dataset, the plot of actual angle and ANFIS pro-duced angle for a complete gait cycle is shown in Fig. 10(a), whileFig. 10(b) illustrate profile of cross correlation between both. TheANFIS output quite closely matches to the real output. The totalnumbers of fuzzy rules are 32 for a complete gait cycle. All thephases were having three inputs, eight fuzzy rules and two tri-angular membership functions. The RMSE for first, second, thirdand four phases was 4.3◦, 4.2◦, 2.2◦ and 0.5◦, respectively. Theonly significant change in the membership function after train-ing was found in the derivative feature. Fig. 11 illustrates thischange. Triangular membership function was found to be the bestamong all, heuristically. The details of all fuzzy rules are givenbelow, Fig. 12.

4. Discussion and conclusion

The ANFIS application to predict the knee joint angle from contralateral knee joint angle with different walking speed is presented.ANFIS proved to be quite successful in mapping the high nonlin-earity between the trajectories of knee joint angle while walking

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Engineering from Garhwal University and Punjab Tech-nical University, respectively. Currently he is purusingthe doctorate from Centre for Biomedical Engineering, IITDelhi. His research area includes Pattern Recognition andSoft Computing application in Prosthesis Design.

764 D. Joshi et al. / Applied Soft

ith different speeds. The results showed the differences in kine-atics within the subjects for same walking speed which gives

trength to the existing concept of “gait signature”. Derivative andurve fitting proved to be potential features; however, the discon-inuity in derivative features during phase transition may lead toudden jerk at those four points in a complete gait cycle. Based onhe analysis in this study the authors recommend high samplingate of knee angle acquisition to minimize the effect of this dis-ontinuity. The application of ANFIS avoids the need of additionalody mounted hardware for hip joint angle measurement [26,27]r foot switch [28,29] for walking speed detection to control therosthetic knee joint. In earlier attempts, researchers have imple-ented ANFIS for knee angle prediction. Only three fuzzy rulesere obtained from simulation data, to predict the knee angle.owever high number of inputs i.e. knee angle and GRF of past

even strides were taken as the inputs [16]. In a recent work inhe direction of developing Echo-Controlled prosthesis four inputs.e. femur angle, tibial angle and their derivatives, were used toredict knee angle of prosthesis side. The developed ANFIS wasaving 14 membership functions and 14 rules and the overall accu-acy of 3.280 [24]. The work presented here achieved the sameccuracy using only one measurement. Thus ANFIS can be a poten-ial tool to predict the prosthetic knee angle from contra lateralimb. Further, the derivative and curve fitting polynomial provedo be a potential feature in minimizing fuzzy rules and mem-ership functions. Higher accuracy can be achieved provided thatNFIS has been trained with large number of data. This approach

eads in designing a cost effective and robust speed adaptive AKrosthesis, that must incorporate wireless network to transfer thengle information from normal limb to prosthesis side. Radio Fre-uency (RF) link is being used for wireless transmission as it ishort range application i.e. not more than 1 m. Only knee angle issed to avoid the redundancy in body mounted sensors and yetost effective. Using only knee measurement systems favors com-ort among amputees. As the information source for the algorithms in the normal leg, it also reduces the chance of fatigue amongatients.

The results depict all the features for prediction of accurateontra lateral prosthetic. Further the derivatives show a poten-ial to discriminate between the phases and hence two successivenee angles will identify the phase and based on the rules of thatarticular phase, the knee angle can be predicted. The results con-rm accurate prediction of contra lateral knee angle using lessumber of inputs and less membership functions, for differentpeeds.

cknowledgements

Authors acknowledge the support of scientist and staff at theefense Institute of Physiology and Allied Sciences (DIPAS), Newelhi for the data collection.

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Deepak Joshi did B.Tech and M.Tech. in Instrumentation

Compu

neering, Punjabi University followed by Masters and

D. Joshi et al. / Applied Soft

Ashutosh Mishra received the B.E. degree from Man-galore University, Karnataka, India and the M.S. degree

from Old Dominion University, Norfolk, VA, in 1999 and2003, respectively. He did Ph.D. degree in the Departmentof Electrical and Computer Engineering, Old DominionUniversity. His research interests include computationalmethods, distributed computation, and bio-electrics.

ting 11 (2011) 4757–4765 4765

Prof. Sneh Anand did her Graduation in Electrical Engi-

Doctorate in Instrumenation Engineering and Biomed-ical Engineering, IIT Delhi respectively. Her researcharea includes Biomedical Instrumentation, RehabilitationEngineering and Transdermal Drug Delivery.