Estimation of Elbow-Induced Wrist Force With EMG Signals Using Fast Orthogonal Search

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 4, APRIL 2007 683

Estimation of Elbow-Induced Wrist Force With EMGSignals Using Fast Orthogonal Search

Farid Mobasser, J. Mikael Eklund*, Member, IEEE, and Keyvan Hashtrudi-Zaad, Member, IEEE

Abstract—In many studies and applications that include directhuman involvement—such as human-robot interaction, control ofprosthetic arms, and human factor studies—hand force is neededfor monitoring or control purposes. The use of inexpensive andeasily portable active electromyogram (EMG) electrodes and po-sition sensors would be advantageous in these applications com-pared to the use of force sensors, which are often very expensiveand require bulky frames. Multilayer perceptron artificial neuralnetworks (MLPANN) have been used commonly in the literature tomodel the relationship between surface EMG signals and muscle orlimb forces for different anatomies. This paper investigates the useof fast orthogonal search (FOS), a time-domain method for rapidnonlinear system identification, for elbow-induced wrist force esti-mation. It further compares the forces estimated using FOS withthe forces estimated by MLPANN for the same human anatomyunder an ensemble of operational conditions. In this paper, theEMG signal readings from upper arm muscles involved in elbowjoint movement and sensed elbow angular position and velocity areutilized as inputs. A single degree-of-freedom robotic experimentaltestbed has been constructed and used for data collection, trainingand validation.

Index Terms—Artificial neural network, electromyography, esti-mation, fast orthogonal search, multilayer perceptron, wrist force.

I. INTRODUCTION

I N MANY applications, such as analysis of sports activities[1], ergonomic design analysis, or teleoperation of robotic

devices [2], the use of force sensors for the measurement of gen-erated limb forces is impractical or inconvenient. Additionally,the high cost of commercially available six degree-of-freedom(6-DOF) force sensors and vulnerability of these sensors tooverload and impact makes alternative methods for muscleor limb force estimation appealing. These methods often useposition and electromyography (EMG) signals which requirecomparatively inexpensive sensors and electrodes.

The generated force in muscles is caused by two processes:activation dynamics and muscle contraction dynamics [3].Muscle contraction dynamics include the mechanical prop-erties of muscle tissues and tendons, which are expressed

Manuscript received October 5, 2005; revised September 16, 2006. This workwas supported in part by Natural Sciences and Engineering Research Councilof Canada, in part by the Institute for Robotics and Intelligent Systems of Net-work of Centres of Excellence, and in part by the Queen’s University AdvisoryResearch Committee. Asterisk indicates corresponding author.

F. Mobasser is with Invenium Technologies Corp., Toronto, ON M2N 6K1,Canada (e-mail: [email protected]).

*J. M. Eklund is with the Faculty of Engineering and Applied Science,University of Ontario Institute of Technology, Oshawa, ON L1H 7K4, Canada(e-mail: [email protected]).

K. Hashtrudi-Zaad is with the Department of Electrical and ComputerEngineering, Queen’s University, Kingston, ON K7L 3N6 Canada (e-mail:[email protected]).

Digital Object Identifier 10.1109/TBME.2006.889190

as force-length and force-velocity relations. The activationdynamics include the voluntary and nonvoluntary (reflex) exci-tation signal and motor unit recruitment level in the muscle. Itis well known that regardless of fatigue, the generated torquein each joint is dependent on muscle activation levels (MALs)and joint angle when in a stationary position [4]. This was firstobserved by Inman et al. [5]. When in motion, joint torque isalso a function of joint angular velocity [6]. Therefore, jointtorque (and force) can be predicted using EMG signals, andjoint angle and velocity measurements. In this paper, it isassumed that the wrist angle is constant. Thus, elbow-inducedwrist force1 can be determined directly from elbow torque.

In the past, nonparametric and parametric model-based ap-proaches have been proposed for muscle force or human jointtorque estimation using EMG signals. Parametric approacheshave used Hill’s muscle model [7], which takes MAL as inputand outputs the muscles generated force as a function of musclelength and contraction speed [6], [8]. Musculoskeletal kine-matic models have also been employed to derive joint torque[9]. Nonparametric methods propose the use of polynomialfunctions or artificial neural networks (ANNs) and have thecapability of accounting for nonlinearities in the EMG-forcerelationship. One significant advantage of nonparametric esti-mation of the EMG-force relationship is that it does not needany knowledge about the muscle and joint dynamics. Clancyet al. [10], [11] proposed the use of a third-order polynomial toestimate the generated torque in elbow joint under isometric2

and quasi-isotonic3 conditions. Misener et al., on the otherhand, used an exponential force/velocity function in additionto a third-order polynomial model to estimate the elbow torque[3]. The prediction was accurate within to 10% for elbowflexion and extension under isotonic4 condition.

On the use of ANN, Sepulveda et al. [12] proposed a multi-layer perceptron ANN (MLPANN) with two layers to estimatejoint moments in human gait. The EMG signals of 16 leg mus-cles were fed into the ANN to estimate joint moments of hip,knee and ankle. Savelberg et al. employed MLPANN for theestimation of a cat leg dynamic tendon force using recordedEMG data and joint kinematic information [13], [14]. In [15],the upper arm EMG signals, and elbow joint angle and velocity

1In this paper, “wrist force” will be used to represent “elbow-induced wristforce.”

2An operational condition involving muscular contractions against resistancewithout movement such that the length of the muscle does not change. In ourcase, under the assumption of negligible tendon stretch, an isometric conditionis created by constraining the elbow angle to a constant value.

3An isometric condition with very slow, constant velocity movement.4An operational condition at which opposing muscles contract and there is

controlled movement. In other words, tension is constant while the lengths ofthe muscles change. In our case, a constant force is applied to the joint whilejoint angle varies.

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684 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 4, APRIL 2007

Fig. 1. Block diagram of FOS and MLPANN force estimators. Componentsdrawn in dashed lines represent the training process.

were utilized by MLPANN to estimate the elbow joint torquesunder isokinetic5 contractions. In a hybrid approach, Wang et al.[16] employed MLPANN to predict the MAL from the EMGsignal recorded from agonist and antagonist elbow muscles.

In this paper, fast orthogonal search (FOS) has been em-ployed for human wrist force estimation. FOS, first developedby Korenberg [17], [18], is a general-purpose estimationmethod which minimizes the mean-square error of the estimatecompared to the target data. However, instead of relying ontime-consuming iterative minimization, as does the commonlyused MLPANN method for backpropagation training, it deter-mines the basis functions and the corresponding coefficientsdirectly in a single iteration. This is accomplished by choosingthe basis functions one at a time, from amongst all the candi-dates, which contributes the greatest reduction in mean squareerror between the estimate and the data. The algorithm thenchooses amongst the remaining candidates, and so on until thestop criteria are met. In comparison with common least-squaresmethods, the advantages of using FOS include developing anaccurate model with fewer terms and being able to includemany additional model terms in the search space while stillproducing a parsimonious final model. With fewer terms, thesystem can be better estimated with less fitting of noise and themodel is more likely to generalize well to novel inputs, albeitdependent on the length and nature of the training data record.FOS has been used in a variety of applications, includingrecursive filtering to remove Gaussian and impulsive noise inimages [19] and compression of speech signals [20]. It has alsobeen investigated for use in magnetic resonance imaging andpositron emission tomography [21], control of nonlinear sys-tems [22], and identification of genes and their functionalitiesfor prediction of therapeutic responses [23].

The performance of the FOS and MLPANN force estima-tors used in a similar experimental setup as shown in Fig. 1are studied under the same set of operational conditions, i.e.,light load, isotonic and isometric. Towards this end, QArm1, our1-DOF exoskeletal robotic arm was constructed for data collec-tion, model identification, and validation.

5An operational condition at which the speed of movement is usually con-trolled, e.g., constant speed, allowing maximal force to be exerted throughoutthe full range of movement.

This paper is organized as follows: in Section II mod-eling methodologies for FOS and MLPANN are introduced.Section III describes the experimental apparatus and the datacollection procedure. Experimental results using MLPANN andFOS are reported and compared in Section IV. In Section V,the practical issues regarding EMG-based force approximationare discussed. Section VI draws conclusions.

II. FOS MODELING METHOD

In this paper, FOS is applied to the identification of the EMG-force relationship in human elbow. In this method, an estimate

of an output time series signal (in this case the wristforce) is found such that

(1)

where is the estimation error and is the discrete timesample index.

The FOS estimate takes the form of a summation of linearor nonlinear functions with coefficients

(2)

where, in the present application, the basis functions arecomposed of the available input signals, such the EMG signals,the joint angle and angular velocity, and combinations of thesesignals as described below and shown in Fig. 1.

The FOS method searches through all the candidate basisfunctions and chooses the most significant contributorsto the estimate in a mean-square error (MSE) sense, as definedby

(3)

where (here and elsewhere) the overline represents the averageover the data record length.

FOS builds the estimate by adding the chosen functions oneat a time using this criterion. The method is based on Gram-Schmidt orthogonal identification, in which orthogonal basisfunctions terms are constructed from the such thatthe estimation takes the similar form

(4)

however, where are the coefficients of the orthogonal basisfunctions , which are orthogonal over the data record, i.e.,

(5)

The orthogonal functions are computed by subtracting fromeach its components “parallel” to previously orthogonal-ized , where

...

(6)

MOBASSER et al.: ESTIMATION OF ELBOW-INDUCED WRIST FORCE WITH EMG SIGNALS USING FOS 685

and

(7)

where is the projection of onto .Due to the properties of orthogonality, it can be shown that

[18]

(8)

and the coefficients that minimize the MSE of the estimate,can be computed from (4), i.e.,

(9)

where is the projection of into .The benefits of such an orthogonal method is that it does not

require any special autocorrelation properties in the input andalso that no error is introduced by the finite duration of the datarecord. However, the creation of the orthogonal functionsis computationally time-consuming and can require consider-able data storage in memory.

Korenberg’s FOS method [17], [18] effectively avoids thisissue by using only certain time averages to compute the MSEreduction associated with each candidate basis function. Thatis to say that only the coefficients of the orthogonalized basisfunctions need to be computed, not the orthogonalized func-tions themselves. Additionally, only those time averages needto be stored, not the many functions of the time series. To dothis, the numerator for (7) can be found without computing the

orthogonal basis functions, when and, using an equation analogous to (6) [18]

(10)

To obtain the denominator for (7), we similarly note that for, from (6) and (7), and exploiting the orthogo-

nality of

(11)

Furthermore, this allows to be computed from (7), whichcan then be substituted back into (10) and (11) to determine theterms required for the recursive solution that is presented.

Once the have been calculated, the values can bedetermined for (4). To this purpose, we can obtain the numeratorfor (9) following (6) as

(12)noting the change in subscript to facilitate the recursion.

Once the terms are found, the terms can beobtained from (9) which gives

(13)

Using the terms found in the decomposition, the MSE (8) ofthe FOS model estimation found using FOS can be equivalentlydescribed using (13) as

(14)

Korenberg [17], [18] noted that, from this, it follows thatif a FOS model of size is extended to one further term

, the MSE will be further reduced by the amount

(15)

where is the MSE reduction of the next term added.An effective search for new candidate terms can, thus, be af-

fected by computing the MSE reduction produced by each can-didate term using (15). The candidate function with the highestMSE reduction is chosen and its coefficient is computedusing the above FOS procedure. The model is, thus, constructedone term at a time until some criteria are met, for instance, ifno further candidates can be found that improve the MSE in ameaningful way, or a certain number of basis functions havebeen selected.

The original nonlinear difference equation coefficients in(2) can then be determined from and from the coefficientsused for orthogonalization, i.e., , according to [18]

(16)

where

(17)

1) Summary of the FOS Algorithm: Assuming that a modelof size has already been identified by FOS from the set of

candidate basis functions (and, thus, there arecandidates remaining), then the choice of the next basis func-

tion is determined by the following.• Calculate the time averages:

— for (the candidatefunctions), and (the functions alreadychosen), which can be computed ahead of time as theydepend only on the input and output data and the choiceof candidate basis functions.


— for , which can alsobe computed ahead of time.

• Compute the MSE reduction (15) for each of thecandidate basis functions remaining at this step, which

requires that— The term of each remaining candidate function be

computed using (7), which uses the values determinedin the previous iteration using (10) and (11).

— The numerator of (15) be computed from (12), which isdetermined based on the previous steps.

— The denominator (15) be computed from (11), which isdetermined based on previous steps.

• Now, with the MSE reduction determined for each ofthe remaining candidate functions from (15), the onecandidate that provides the greatest MSE reduction, i.e.,

, , is chosen andadded to the model.

• Finally, the coefficient for the basis function chosenis computed from (13), (16), and (17)

Therefore, the next basis function is chosen, and the valuesused at this step are stored for use in the next step. This con-tinues until either no more basis functions remain that can pro-vide a significant reduction in MSE, or a predetermined numberof basis functions have been chosen. A detailed description ofthis algorithm can be found in [18].

2) Choice of Candidate Basis Functions: The choice of non-linear basis functions may have significant effect on overfittingof the data and on the extrapolation of the model to new data.For example, in polynomial estimation using the Taylor The-orem, one is able to fit a data set to an arbitrate accuracy if suf-ficient polynomial terms are included. As the number of termsincreases, however, the resultant estimate will typically becomeless accurate at estimating data outside of the training set and/orthe operating region of the system being modeled. Lower ordermodels, however, may provide poorer accuracy on the trainingdata set, but better accuracy on the testing set when comparedto a higher order model.

As an alternative, instead of using polynomial terms,we could instead use inverse exponential terms such as

. In fact, these fractional polyno-mial functions (including the square root) are modified to beodd, real functions by taking the power of the absolute valueof the function input, then multiplying the result by the sign ofthe input. This results in a somewhat poorer estimate within thetraining range, but potentially performs much better outside ofthe training range compared to the polynomial estimate. In thispaper, the modified square root function, sigmoid function andquadratic functions with limits on them are used. In the caseof the limited quadratic function, the value of the limit is anadditional parameter to be estimated, however, in this paper thelimit value is fixed.

With regard to the number of basis functions chosen, thereexist methods for estimating the optimal number of model termsto include for linear system identification such as the Akaikeinformation criteria (AIC), Bayesian information criteria (BIC)and variants. For classification models there exist methodssuch as Vapnik Chervonenkis (VC) dimension. The extensionof these to methods nonlinear models is problematic and anarea of much interest [24], [25], however, beyond the scope ofthis paper. This paper uses cross-validation [26] to study the

Fig. 2. Picture of the 1-DOF experimental setup (QArm1) with a subject.

effect of the nature of basis functions and their number chosenthrough the training and validation results.

III. EXPERIMENTAL SETUP AND PROCEDURES

A. Experimental Setup

A 1-DOF robotic testbed (QArm1) has been designed and de-veloped in collaboration with Sensory Motor Systems Groupat Queen’s University to conduct force estimation experimentsusing EMG signals. As shown in Fig. 2, the apparatus is com-posed of a platform accommodating a Maxon dc motor, a 4:1cable-driven power transmission system, and an aluminum baron which subject’s arm is placed. In this design, the subject’supper arm is placed in a fixed position brace and the wrist in asecond brace attached to a pivoting bar through an ATI Gamma6-DOF force/torque sensor. The force/torque sensor is made ofsilicon strain gauges with nearly zero noise distortion and itdisplays extremely high stiffness of . Thus itis used as our “gold standard” force measurement. The axis ofrotation of the bar pivot is aligned with the elbow’s axis of ro-tation. The high resolution encoder signal provides the motorshaft angle, which is proportional to elbow angle. The resolu-tion of elbow angle measurement is 1/4000 of a degree. The ap-paratus can apply up to 6.32 Nm continuous torque to the elbowjoint, which is mapped to about 16 N at the wrist. The QuanserWincon/Venturcom RTX real-time control system is employedto collect data and control at the sampling rate of 1 kHz.

To collect EMG signals from upper arm muscles, active elec-trodes containing differential amplifiers (to cancel the effect ofenvironmental electromagnetic interference) from Simon FraserUniversity were employed. The sensors lower cutoff frequencywas 30 Hz and upper cutoff frequency was 500 Hz with peak-to-peak output noise of 10 mV at the maximum gain of 2000. Thedistance of the electrode plates was 15 mm and each plate wascone shaped with diameter of 4 mm. The electrodes were ori-ented parallel to muscle fibers and placed between the belly ofeach muscle and its ends, as indicated in Fig. 3. For experiments,a thick pad was used between the brace and the subject’s armfor subject’s comfort and to dampen the pressure exerted by thebrace. In addition, the EMG sensors and the arm were wrappedwith a thin spongy tape to keep the sensors in contact with skin.


Fig. 3. Active electrode placements on upper arm muscles, (a) triceps, (b) bi-ceps, and (c) brachioradialis (anatomy: courtesy of J. R. Cram, G. S. Kasman,and J. Holtz [28], printed with permission).

In order to show the location of the sensors clearly, the thick padand the spongy tape wrap are not displayed in Fig. 2. Our testshave shown that the potential motion artifacts produced by themechanical contact between the sensors and the pad or the tapeis negligible.

The recorded raw EMG data was passed through a linear en-velope filter [27]. To this end, the recorded EMG was digitizedusing a 14-bit analog-to-digital converter. Then the bias of theEMG was detected by applying a moving average filter, andwas removed from the original signal. Afterwards, the resultingsignal was rectified and passed through a second moving av-erage filter with a size of 300. This produced 150 ms of delay inthe final EMG signal. The filter length and the resulting delaywas chosen to match the delay between the collected EMG6

signal (or motor nerve excitations) and the force generated bythe muscle [3].

B. Experimental Procedure

The EMG electrodes were attached to the bicep brachii prox-imal to the elbow, tricep brachii long head, and brachioradialismuscles, as illustrated in Fig. 3. The subject’s shoulder and wristwere placed in the arm braces ensuring that the upper arm wasstabilized and the elbow joint axis coincided with the bar rota-tion axis. The shoulder was stabilized at 90 abduction, 15 hor-izontal adduction and neutral pronation-supination. Informedconsent was received from each subject and the experiment pro-tocol was explained to each subject prior to the experiment. Thesubjects were asked to relax all muscles not directly involved inelbow flexion/extension.

The level of EMG readings is dependent on skin impedance atthe electrodes location, which may vary between experimentalsessions. To compensate for this variability, the EMG readingshave to be normalized for each recording session and after elec-trode placement. A widely used EMG normalization method ismaximum voluntary contraction (MVC) method [6], in whichthe subject is asked to maximally contract the muscle under

6Note: From this point forward “EMG” will refer to “processed EMG,” unlessotherwise indicated.

study. The corresponding EMG reading is used for normaliza-tion of the rest of EMG readings from that muscle. The MVCmethod was employed for EMG normalization in the first place,but did not provide satisfactory estimation results. In fact, usingthe MVC is problematic as there is no consistent guarantee thatthe subject is actually generating the maximal force [6].

In an alternate approach [29], at the beginning of eachrecording, a 6 Nm torque was applied by the Qarm1 to theelbow joint in flexion and extension directions while the subjectwas asked to keep the elbow angle in 0 flexion. The averageof the recorded EMG was then used for the normalization ofthe EMG data: bicep brachii and brachioradialis (in flexion)and lateral tricep brachii (in extension). This method producedbetter results in comparison to the MVC method. For operationoutside the laboratory environment, where QArm1 or any othermanipulandum is not available, the subject can be asked to holda specific weight for EMG normalization. Afterward, in eachexperiment, the joint kinematic data and muscle EMGs wererecorded under the following sequence of conditions.

• Light Load: No torque was applied to elbow joint byQArm1 and the subject was asked to move her/his arm ina random pattern. The only load that was sensed by thesubject was the light inertia of the robotic arm.

• Isotonic: The QArm1 applied constant torque to the sub-ject’s elbow joint and the subject moved her/his arm inrandom pattern. Equivalent wrist force level of 5 and 10N were applied to the joint both in flexion and extensiondirections.

• Isometric: The subject performed a number of isometricflexion and extension at the elbow extension of 0 and 30 ,while the QArm1 was held fixed by the subject’s otherarm as in [4], [10], and [15]. The level of force applied bysubject was variable and arbitrary.

The data was collected from the right arm of three male andtwo female subjects with an average age of 26 years. The sub-jects had no known neuromuscular deficits of the right shoulder,arm or hand. Each subjects was tested in three sessions at threedifferent times. In each recording session, experiments wereconducted four times and four sets of data were recorded. Theoutlier data sets that mainly had faults in EMG readings wereexcluded. Therefore, up to a maximum of twelve data sets werecollected and kept from each subject for analysis. Care wastaken to ensure that subjects generated nonspecific random pat-tern force with flat frequency response up to the maximum op-erating frequency 3 Hz. A sample data set, from subject M1, isshown in Fig. 4. Each set includes processed EMG signals frombiceps, triceps and brachioradialis muscles, elbow angle, elbowangular velocity, actuator torque and the measured wrist forcefor four different phases of each experiment; i.e., normalization,light load, isotonic, and isometric.

IV. EXPERIMENTAL RESULTS

1) FOS Basis Functions: Using the FOS modeling methoddescribed in Section II, five subsets of basis functions wereconsidered. The first subset of 17 basis functions, which wascommon to all tests, contained linear terms and cross terms withand without the sine and cosine functions, as seen in the firstblock of Table I. Combined with this common set were one


Fig. 4. Sample recorded data set from subject M1.

of the four subsets of functions, as seen in the other blocks ofTable I, each based on different nonlinear terms: (a) quadratic,(b) quadratic followed by a limit function, (c) square root, and(d) sigmoid function. A fifth test (e) was performed with all ofthe functions in Table I included, specifically the common func-tions and (a)–(d). Thus, the five tests included 23, 29, 29, 29, and59 basis functions for tests (a)–(e), respectively.

2) MLPANN Architecture and Training: In this paper, thecommonly used MLPANN was employed as a benchmark toevaluate and compare the performance of the proposed FOS-based force estimator. The selected network features two hiddenlayers with hyperbolic tangent sigmoid and linear functions forthe hidden layers and the output layer, respectively. The inputsof the network were the EMG signals recorded from upper armmuscles: bicep brachii, tricep brachii and brachioradialis, andelbow joint angle and angular velocity. The network output wasthe estimated wrist force.

Backpropagation with Levenberg-Marquart (LM) optimiza-tion method was used for training the network. The LM method,which was implemented in MATLAB using TRAINLM func-tion, is commonly used in situations involving function approx-imations with less than a hundred neuron weights where accu-racy is paramount [30]. For training the networks, the outputtorque, the elbow angle and the elbow angular velocity werenormalized to [ 1 1] with respect to their expected dynamicrange, which was similar for all data sets. The EMG signals, onthe other hand, were normalized using their range of variationsidentified in the same session for the specific 6 Nm torque pro-file applied by QArm1 in the normalization phase. Therefore,the normalized EMG signals were not limited to [ 1 1]. The

TABLE IBASIS FUNCTIONS USED. THE COMMON FUNCTIONS PLUS ONE OR ALL

SUBSETS OF THE NONLINEAR TERMS WERE USED. E , E , AND E ARE

THE BICEP, BRACIORADIALIS, AND TRICEP EMG SIGNALS, RESPECTIVELY. �IS THE ELBOW JOINT ANGLE, _� IS THE ELBLOW JOINT ANGULAR VELOCITY,

AND “OFFSET” IS THE BIAS TERM. THE EXPRESSION x REPRESENTS THE

LIMITED SQUARE FUNCTION, sigm THE SIGMOID FUNCTION, ANDp

THE

MODIFIED SQUARE ROOT FUNCTION AS DESCRIBED IN SECTION II-A

reason for this normalization is to benefit from the more sen-sitive region of the sigmoid activation function. To avoid over-training, the data set was also down-sampled by a factor of 10.Validation sets were normalized to the same [min max] rangedetermined for training. Different number of layers and nodeswere examined for MLPANN with two hidden layers. The ex-periments showed that 4 nodes in the first layer and three nodesin the second layer provided the best generalization and the mostconsistent performance.

To avoid networks from being trapped in local minima intraining process, ten networks were trained for 1000 epochs withvery small target training goal (smaller than the lowest estima-tion error that the networks could meet). The best performingnetwork was chosen and trained for an additional 1000 epochs.

3) FOS and MLPANN Training: All the 12 data sets fromeach subject were used as training sets. For each model training,validation was done with the remaining 11 data sets. The trainedmodel that provided the best validation was recorded and usedto represent the dynamic model of the subject.

The time consumed for the training of the two models withapproximately 150 000 samples on a Pentium 4 2.4-GHz CPUis shown in Table II. The training for FOS was approximately


TABLE IICONSUMED TIME FOR TRAINING FOS AND MLPANN OBSERVERS

350–5000 times faster than that of MLPANN, which is a sub-stantial advantage when the number of sample points in the datais high. The computation time required for FOS increases lin-early with the number of data points used, increases by the orderof with the number of basis functions searched, and lin-early with the number of basis functions chosen. The compu-tation time for MLPANN increases linearly with the number ofpoints and epochs, and increases with the order offor a network with nodes in the second layer and nodes inthe first layer. The saved training time can be used for a quickcheck of the quality of the collected data, faster selection of amore generalizable and accurate model, and training models formultiple subjects in a short duration of time. Once trained, theonline calculation of ANN and FOS outputs take a fraction ofa second since it only requires a forward pass of input throughthe models.

4) Evaluation Criteria: To validate the trained models, eachmodel was evaluated against all data sets with the two criteria,relative mean square error percentage (MSE%) and average ab-solute error (AAE) formulated as

(18)

(19)

where and are the measured and the estimated wrist force,respectively, and is the number of samples. Since the valuesof measured force in light load condition were small, insteadof MSE%, AAE was used for evaluation, especially for thiscondition.

5) FOS Results: In order to study the effect of the number ofbasis functions included in the model, the FOS algorithm was setto select the best 5, 7, 10, 15, or 20 basis functions for inclusionin the model for each individual data set and the appropriatecoefficients were determined.

As can be seen from the training results for Subject F1 inFig. 5, the MSE% decreases steadily with the added number ofbasis functions included in the model, and is largely indifferentto the choice of the nonlinear function subset. The results simplysuggest increase in the number of basis functions to improve theresults. However, this does not apply to the validation results inFig. 5, where a minimum is clearly present at 10, 15, 7, 7, and10 basis functions for the quadratic, modified square root, lim-ited quadratic and sigmoid nonlinear function subsets, respec-tively. The correlation between the validation results and thenumber of functions can be attributed to overfitting the model,and larger models are clearly not the best choice when it comesto validation.

The sigmoid and square root functions appear to be the bestchoices for candidate basis functions, based on the validation

Fig. 5. MSE% of the FOS training (solid lines) and validation (dashed lines)results for subject F1 as function of number of basis functions and choice of basisfunctions. The basis function sets are quadratic, square root, limited quadratic,sigmoid, and all functions included. Note the correlation of reduction in trainingMSE% to the number of basis functions used, and the lack of correlation to thechoice of basis functions set. Also compare this to the absence of correlationbetween the validation MSE% and the number of basis functions.

results for the subsets investigated. As seen in Fig. 5, the sig-moid function provides the best MSE% overall with 10 or morebasis functions, with and is clearly robust tooverfitting. The square root, however, is noticeably better withfewer basis functions and nearly as good with 10 or more. Theother subset choices are nearly as good for models with 7 or 10terms but then deteriorate significantly with more terms in theirMSE%.

We also note that there does not appear to be any benefit fromincluding all of the possible basis functions in the FOS searchspace as this produces one of the poorest validation results, de-spite providing the best training result. Additionally, the largersearch space requires additional computation time, which couldbe reduced by excluding rarely chosen terms. This does, how-ever, provide some insight into which basis functions are se-lected by FOS, as shown in Table III, where the frequency ofselection of basis functions is given when all are included in thesearch space. Here we see that 5 functions were never included,and these are amongst the simplest functions and perhaps mostlikely to be chosen by a human modeler. As well, more than onethird of them were included 10% or less number of the time.If these were excluded from the search, the FOS identificationtraining would take roughly 50% less computational time.

6) Comparison to MLPANN Results: The training and vali-dation MSE%, MSE% standard deviation, and AAE results forthe five subjects are presented in Table IV.

The results of training with “full-length data” (including lightload, isotonic, and isometric) are reported in the left hand sec-tion of Table IV where the MSE% are also reported separatelyfor the three subsets of the data. Examples of the time seriesplots of measured and estimated force for Subject M1 are shownin Fig. 6. We note that in training and in validation the lightload condition reports MSE% values that are much larger thanthe other subsets, which is a result of the measured forces being


TABLE IIIFREQUENCY OF BASIS FUNCTION SELECTION FOR SUBJECT M3 WITH ALL NONLINEAR FUNCTIONS INCLUDED

TABLE IVTHE MSE% FOR BOTH TRAINING AND VALIDATION USING THE FULL DATA SET AND SUBSET DATA. THE TRAINING RESULTS ARE PRESENTED AS AVERAGE

MSE%, AND THE VALIDATION RESULTS ARE PRESENTED AS TRIPLETS OF AVERAGE OF MSE% (STANDARD DEVIATION OF MSE%) [AAE]

considerably smaller in this case. Therefore, the AAE, which isan absolute performance index, serves as a better performancecriterion for this particular subset with relatively small values.As can be seen, the validation results in the isometric conditionare significantly better than those obtained under isotonic andthe light load conditions. In the 20 cases trained with the fullset of data, FOS performed as well or better than MLPANN in65% of the cases when comparing MSE% and 90% of the caseswhen comparing AAE.

Finally, both FOS and MLPANN were trained and validatedfor each subset (isometric, isotonic and light load) using onlythe corresponding subset of the data for the particular task. The

results are reported in the right hand sections of Table IV. A timedomain example is plotted in Fig. 7 in which the FOS validationresults are shown for the same example data as in Fig. 6(c)–(e).Here we see that the subset training improved the validation re-sult very significantly for the light load case, quite noticeablyfor the isotonic case, and not significantly for the isometric case.This observation is confirmed more broadly in Table IV whereit is also clear that performance of the models improved signif-icantly after subset training in almost all cases. Using averageMSE% as a measure in these cases, FOS was outperformed byMLPANN 67% of the time, but it was FOS outperforming ML-PANN 67% of the time when comparing AAE.


Fig. 6. FOS and MLPANN validation results for subject M1. The FOS and MLPANN results for cross-validation on models identified from the “full data sets”are shown in (a) and (b), respectively, in which the error is shown above the actual and estimated forces. In (c), (d), and (e) samples are shown in detail of the sameresults in the light load, isotonic and isometric subsets and the FOS result appears above the MLPANN.

Overall, FOS has demonstrated superior performance com-pared to MLPANN under full-length training, while they havecomparable performance in the subset training. In addition, FOStraining was two to three orders of magnitude faster than ML-PANN.

7) Comparison of FOS to Radial Basis Function Neural Net-works (RBFANN): Considering the model structure for FOS,one can see close similarities between FOS and RBFANN [27].Therefore, RBFANN would potentially make the best type ofANN for comparison with FOS. However, MLPANN has beenchosen, since the objective of this paper has been to compareFOS with the most commonly used ANN. Nevertheless, we triedRBFANN on the data collected from subjects F1 and F2. Basedon the average MSE% for validation we found that RBFANNwith 40 nodes provides the best generalization. Comparing theRBFANN results tabulated in Table V with the correspondingFOS results repeated from Table IV, one can see that the resultsare similar for the two methods, with FOS being slightly betterin most categories and significantly better in terms of AAE inalmost all cases. In terms of training speed, we found that RBFwas 5 to 6 times faster than MLPANN, yet still about 100 timesslower than FOS.

V. DISCUSSION

The MAL is a function of excitation signal firing rate and re-cruitment of muscle fibers. The measured EMG is an ensembleof the motor unit action potentials under electrode and is verydependent on the electrode configuration, placement and signal

preconditioning. Therefore, the recorded EMG is not a total rep-resentation of MAL. This factor and stochastic property of EMGsignal affect the repeatability of EMG signal with respect to gen-erated force, which is a challenge in force estimation based onEMG data. The position of electrodes and fidelity of EMG sig-nals play an important role in the accuracy of estimations [15].One reason for this is the crosstalk readings from adjacent mus-cles, and the sensor location should be selected to minimize theeffect of this crosstalk [12], [31]. In fact, the EMG signal of thebrachialis muscle was initially recorded but was not includedin our final experiments due to the contamination by crosstalkfrom the biceps and triceps muscles. In applications in whichthe contribution of the muscle of interest is significant and theEMG signal from that muscle cannot be eliminated, double dif-ferential technique using three surface electrodes can be used toremove the effect of cross-talk [6]. In anisometric motion, arti-facts which are caused by the movement of muscle under elec-trode are often a problem. Another issue that is not taken intoconsideration and needs future investigation is muscle fatigue.In this paper, all of the estimations were done under nonfatiguecondition.

We note that the model generated for each subject may not beapplicable to the other subjects due to the differences in positionof EMG electrodes relative to the motor units, and individualvariations in muscle fiber types, muscle volume, muscle length,difference in motor unit recruitment strategies, the amount offat underneath skin and geometrical properties of the joint [13].Therefore, the model should be generated for each individual.


Fig. 7. The FOS validation results in which the models were trained with the specific data subsets: light load, isotonic and isometric. These results can be comparedto the detailed results reported in Fig. 6(c)–(e) for full data training. (a) Light load training and validation; (b) isotonic sample; (c) isometric sample.

TABLE VCOMPARISON OF THE MEAN MSE% FOR VALIDATION USING FOS AND RBFNN. THE RESULTS

ARE PRESENTED AS AVERAGE OF MSE% (STANDARD DEVIATION OF MSE%) [AAE]

The FOS results showed that the choice of basis functionsand the number of functions to include was very important tothe final validation of the model. While the best validation re-sults were found to be with sigmoid functions for larger models,which were also the most accurate, smaller models with squareroot functions were nearly as accurate and robust to modelsize and overfitting. Other nonlinear terms produced similaraccuracy but only for a small range of model sizes, specificallyaround 7 or 10. This leads us to the belief that the best choicefor a model structure for rapid identification would use themodified square root function combined with the sinusoidalfunctions and cross terms as detailed above. This provides agood balance between accuracy and robustness to model orderestimation and size. However, the sigmoid function can provideslightly better performance with larger model sizes. Finally,we note that increasing the search space with the inclusion ofall the nonlinear model terms in the search space degraded thevalidation results, despite improving the training result.

VI. CONCLUSION

This paper investigates the use of the FOS method for elbow-induced wrist force estimation while arm motion is restricted toelbow extension and flexion in horizontal plane and under threeoperating conditions: isometric, isotonic and light load. Theseresults are evaluated with different nonlinear basis functions andcompared to the estimates made using MLPANNs.

The nonlinear basis functions investigated for use with FOSincluded quadratic, limited quadratic, modified square rootand sigmoid functions. The selection of these functions andthe number of functions to be included in the models wereinvestigated. In training, the MSE% reduced as the numberof basis function increased with all functions, however, theseimprovements did not carry over to the validation results. Invalidation, the quadratic function provided the best MSE% andstandard deviation results (expect for the case where all func-tions were included) when 10 basis functions were chosen byFOS. However, if FOS was allowed to choose more functionsthe validation results would deteriorate—quite significantly in

some cases. With the modified square root function and thesigmoid function the validation results also favored 10 basisfunctions as the optimal number, but they did not deterioratesignificantly when a larger model was allowed. Including allthe subsets of basis functions in the FOS search yielded thebest training result, but one with high sensitivity to overfittingas revealed by the poor validation result.

Both FOS and MLPANN were able to predict the highly non-linear relationship between joint parameters (EMG, angle andvelocity) and generated force, and could generalize intra-ses-sions with for FOS and 32% for MLPANNfor training with full-length data (i.e., the concatenation of lightload, isometric and isotonic data). Additionally, FOS demon-strated much faster training and provided more accurate resultsthan MLPANN in most cases. The estimation performance ofboth methods, FOS and MLPANN, were further improved whenthey were trained with the corresponding subset data. This wasparticularly true for the light load condition. This suggests that ifthe nature of the task is known a priori, then very good estimatesof the force can be made in all of these conditions. Furthermore,FOS is able to determine the EMG based force estimation func-tions rapidly enough to enable individual training.

The experimental results show that kinematic and EMG sig-nals can be effectively used to estimate elbow-induced forceat human arm wrist for some types of contractions without theneed for expensive or bulky force/torque measuring device. Thedeveloped FOS model can further be employed to investigate theengagement of each upper arm muscle in the end-point force fordifferent types of limb actions. The proposed FOS observer canalso be used as a base to further develop a force observer formonitoring and analysis of athletes’ performance in sport activ-ities such as rowing, in ergonomic design for office and factoryworkers or remote operation control of robotic devices.

ACKNOWLEDGMENT

The authors wish to thank Dr. S. Scott and his group fortheir collaboration and support in the design and construction ofQArm1 and the volunteer subjects for their help and patience.


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Farid Mobasser received the Ph.D. degree inelectrical engineering from Queen’s University,Kingston, ON, Canada, in 2006. He received theM.Sc. and B.Sc. degrees in computer engineeringfrom Sharif University of Technology (SUT),Tehran, Iran, in 1997 and 1999, respectively.

He has worked with eight different firms andcompanies from 1994 through 2001. He is currentlythe President and CEO of INVENIUM TechnologiesCorporation, Toronto, ON, Canada. His interests aretelerobotics, computer vision, mobile robots, and

biomedical robotics. In 1999, he was a member of the SUT championshipmiddle-sized RoboCup team.

In 2001, the SUT rescue robot research team Dr. Mobasser led won the besttechnical design award in the RoboCup/AAAI rescue robot competition.

J. Mikael Eklund (S’98–M’03) received the B.Sc.degree in electrical engineering in 1989 and the M.Sc.and Ph.D. degrees in electrical and computer engi-neering in 1998 and 2003, respectively, from fromQueen’s University, Kingston, ON, Canada.

He worked for CAE Electronics Ltd until 1996 as aSimulator Flight Controls Engineer and he was a Vis-iting Postdoctorial Scholar in the Department of Elec-trical Engineering and Computer Sciences at the Uni-versity of California, Berkeley, until 2006. Since July2006, he has been an Assistant Professor at the Uni-

versity of Ontario Institute of Technology, Oshawa, ON, Canada. His researchinterests include nonlinear system identification, nonlinear control, heathcareinformation and communication technology, and autonomous systems and ve-hicles.

Keyvan Hashtrudi-Zaad (S’94–M’00) received theB.Sc. degree in electrical engineering from SharifUniversity of Technology, Tehran, Iran, in 1991;the M.A.Sc. degree in electrical and computer engi-neering from Concordia University, Montreal, QC,Canada, in 1994; and the Ph.D. degree in electricaland computer engineering from University of BritishColumbia, Vancouver, BC, Canada, in 2000.

He held a consulting position with Motion Met-rics Inc., Vancouver, on a project in design and devel-opment of a dynamic payload monitoring system for

heavy-duty hydraulic machines. Since 2001, he has been with the Departmentof Electrical and Computer Engineering of Queen’s University, Kingston, ON,Canada as an Assistant Professor. His research interests include control systemsdesign for telerobots and haptic interfaces, medical applications of haptics andvirtual environments, dynamics identification, and biomedical robotics.

Dr. Hashtrudi-Zaad has served on organizing and program committees of theIEEE conferences CCA’05, ICMA’05, and IROS’05.

Estimation of Elbow-Induced Wrist Force With EMG Signals Using Fast Orthogonal Search

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