Assessment of Muscle Fatigue using a Probabilistic Framework for an EMG-based Robot Control Scenario

Transcription

1 Assessent of Muscle Fatigue using a Probabilistic Fraework for an EMG-based Robot Control Scenario Panagiotis K. Arteiadis and Kostas J. Kyriakopoulos Abstract Huan-robot control interfaces have received increased attention during the last decades. With the introduction of robots in every-day life, especially in developing services for people with special needs i.e. elderly or ipaired persons, there is a strong necessity of siple and natural control interfaces. In this paper, electroyographic EMG signals fro uscles of the huan upper lib are used as the control interface between the user and a robot ar. EMG signals are recorded using surface EMG electrodes placed on the user s skin, letting the user s upper lib free of bulky interface sensors or achinery usually found in conventional huan-controlled systes. The proposed interface allows the user to control in real-tie an anthropoorphic robot ar in three diensional 3D space, by decoding EMG signals to otion. However, since EMG changes due to uscle fatigue are present in this kind of control interface, a probabilistic fraework has been developed, which can detect in real-tie the uscle fatigue level. By coplying to those fatigue-related signal changes, the proposed ethod can provide accurate decoding of otion through long periods of tie. The syste is used for the continuous control of a robot ar in 3D space, using only EMG signals fro the upper lib. The ethod is tested for a long period of operation, proving that uscle fatigue does not affect the decoder accuracy. The efficiency of the ethod is assessed through real-tie experients including rando ar otions in 3D space. I. INTRODUCTION Although, robots cae to light approxiately 50 years ago, the way huans can interface with the and finally control the is still an iportant issue. The huan-robot interface plays a role of the utost significance, especially since the use of robots is increasingly widening to everyday life tasks e.g. service robots, robots for clinical applications. A large nuber of interfaces have been proposed in previous works. However, ost of the previous works propose coplex echaniss or systes of sensors, while in ost cases the user should be trained to ap his/her action i.e. three diensional 3D otion of a joystick or a haptic device to the desired otion for the robot. In this paper a new ean of control interface is proposed, according to which, the user perfors natural otions with his/her upper lib. Surface electrodes recording the electroyographic EMG activity of the uscles of the upper lib are placed on the user s skin. The recorded uscle activity is transfored to kineatic variables that are used to control the robot ar. EMG signals have often been used as control interfaces for robotic devices. However, in ost cases, only discrete P. K. Arteiadis and K. J. Kyriakopoulos are with the Control Systes Lab, School of Mechanical Eng., National Technical University of Athens, 9 Heroon Polytechniou Str, Athens, , Greece {parte, kkyria}@ail.ntua.gr control has been realized, focusing only for exaple at the directional control of robotic wrists 1], or at the control of ulti-fingered robot hands to a liited nuber of discrete postures 2]. Quite recently Thakor et al. 3] achieved to identify 12 individuated flexion and extension oveents of the fingers using EMG signals fro uscles of the forear of an able-bodied subject. However, controlling a robot by using only finite postures can cause any probles regarding soothness of otion, especially in the cases where the robot perfors every-day life tasks. Therefore, effectively interfacing a robot ar with a huan entails the necessity of continuous and sooth control. An iportant factor that is present in the EMG-based controlled systes, though never been investigated until now, is the uscle fatigue, and how it affects the EMG signal decoding. Muscle fatigue is reflected by certain changes in its electroyogra signal 4]. All the algoriths that have been proposed in the past use stationary odels for translating EMG signals to otion. Therefore, EMG changes due to fatigue are not incorporated in the previously used odels, aking the aforeentioned ethods applicable only for short tie periods. In this paper, a uscle fatigue-dependent ethodology for controlling an anthropoorphic robot ar using EMG signals fro the uscles of the upper lib, is proposed. Surface EMG electrodes are used to record fro 11 uscles of the shoulder and the elbow. The syste architecture is divided into two phases: the training and the real-tie operation. During the training phase, the user is instructed to ove his/her ar in rando patterns with variable speed in the 3D space. A position tracking syste is used to record the ar otion during reaching. The procedure lasts for 4 inutes, with no resting periods, in order to investigate uscle fatigue and EMG changes due to fatigue. Four DoFs are analyzed i.e. two for the shoulder and two for the elbow. To tackle the diensionality proble, the activation of the 11 uscles recorded and the 4 joint angle profiles are represented into two low-diensional spaces via the appropriate technique. The apping between those two low-diensional spaces is realized through a linear odel whose paraeters are identified using the previously collected data. Changes in EMG signals due to uscle fatigue are onitored for all the recorded uscles. Then, through the appropriate ultivariate odeling and a Bayesian classifier, the condition of the uscles with respect to their fatigue is identified. Having represented the uscles condition in discrete phases of fatigue, a set of odels are trained instead of one stationary odel. In this way, the changes in EMG signals

2 Fig. 1. The controlled robot ar is equipped with two rotational DoFs at the shoulder, and two at the elbow. due to fatigue are incorporated into the decoding odel, since a set of fatigue-dependent odels is trained instead of one. Therefore, the accuracy of the decoding ethod is not affected by uscle fatigue, and the ethodology can be used for long periods of tie without any efficiency deterioration. As soon as the training phase has finished, the real-tie operation phase coences. A control law that utilizes these otion estiates is applied to the robot ar actuators. In this phase, the user can teleoperate the robot ar in real-tie. The efficacy of the proposed ethod is assessed through a large nuber of experients, during which the user controls the robot ar in perforing rando oveents in the 3D space. The rest of the paper is organized as follows: the proposed syste architecture is analyzed in Section II, the experients are reported in Section III, while Section IV concludes the paper. II. MATERIALS AND METHODS A. Background and Proble Definition The otion of the upper lib in the 3D space will be analyzed, not including though the wrist joint for siplicity. Therefore the shoulder and the elbow joints are of interest. Since the ethod proposed here will be used for the control of a robot ar PA-10, Mitsubishi Heavy Industries, equipped with 2 rotational DoFs at each of the shoulder and the elbow joints as shown in Fig. 1, we will odel the huan shoulder and the elbow as having two DoFs too, without any loss of generality. In fact, it can be proved fro the kineatic equations of a siplified odel of the upper lib, that the otion of the huan shoulder can be addressed by using two rotational DoFs, with perpendicularly intersecting axes of rotation. The elbow is odeled with a siilar pair of DoFs corresponding to the flexion-extension and pronationsupination of this joint. Hence, 4 DoFs will be analyzed fro a kineatic point of view. It ust be noted that a detailed kineatic odel of the upper lib is out of the scope of this paper, since the robot to be controlled is equipped with a liited nuber of DoFs for the joints analyzed. For the training of the proposed syste, the otion of the upper lib should be recorded and joint trajectories should be extracted. For this scope, a agnetic position tracking syste was used, equipped with two position trackers and a reference syste, with respect to which the 3D position Fig. 2. The user oves his ar in the 3D space. Two position tracker easureents are used for coputing the four joint angles. The tracker base reference syste is placed on the shoulder. of the trackers is provided. In order to copute the 4 joint angles, one position tracker is placed at the user s elbow joint and the other one at the wrist joint. The reference syste is placed on the user s shoulder. The set-up as well as the 4 odeled DoFs are shown is Fig. 2. Let T 1 x1 y 1 z 1, T2 x 2 y 2 z 2 the position of the trackers with respect to the tracker reference syste. Let q 1, q 2, q 3, q 4 the four joint angles odeled as shown in Fig. 2. Finally, by solving the inverse kineatic equations the joint angles are given by: where q 1 arctan2 ±y 1, x 1 q 2 arctan2 ± x y2 1, z 1 q 3 arctan2 ±B 3, B 1 q 4 arctan2 B1 2 + B2 3, B 2 L 1 B 1 x 2 cosq 1 cosq 2 + y 2 sin q 1 cosq 2 z 2 sin q 2 B 2 x 2 cosq 1 sin q 2 y 2 sin q 1 sinq 2 z 2 cosq 2 B 3 x 2 sinq 1 + y 2 cosq 1 2 where L 1 the length of the upper ar. The length of the upper ar can be coputed fro the distance of the first position tracker fro the base reference syste, while the length of the forear L 2 can be coputed fro the distance between the two position trackers. It ust be noted that since the position trackers are placed on the skin and not in the center of the odeled joints, the lengths L 1, L 2 ay vary as the user oves the ar. However, it was found that the variance during a 4 inute experient was less than 1c i.e. approxiately 3% of the ean values for the lengths L 1, L 2. Therefore, the ean values of L 1, L 2 for a 4 inute experient were used for the following analysis. Regarding uscle recordings, a group of 11 uscles, ainly responsible for the analyzed otion, is recorded: deltoid anterior, deltoid posterior, deltoid iddle, pectoralis ajor, teres ajor, pectoralis ajor clavicular head, trapezius, biceps brachii, brachialis, brachioradialis and triceps brachii. 1

3 B. Muscle Fatigue Related EMG Changes It is widely reported in the bioechanics and physiology literature that prolonged or repeated contractions of skeletal uscles lead to ipaired uscle function, i.e. developent of fatigue 4]. It has been also reported that EMG signal changes with uscle fatigue 4]. In this work, the way these changes are illustrated in the EMG recordings will be investigated in order to build a ethod able to identify uscle condition with respect to fatigue in real-tie. The quantification of uscle fatigue will then lead us to build a set of odels for decoding EMG signals to otion, in such a way that EMG changes will not affect the decoding accuracy. As noted before, the syste requires a training period of 4 inutes, without resting periods. During this period, EMG signals fro 11 uscles are recorded. After signal preprocessing, a set of signal features are coputed. These are listed below: Integral of absolute value IAV Zero crossing ZC Variance VAR For details about these signal characteristics the reader should refer to literature 5]. The calculation of the previously defined signal features for the training period of 4 inutes, showed that there is an increase in their values with respect to the experient tie that is related to uscle fatigue. Siilar behavior was noticed for all the recorded uscles. C. Muscle Fatigue Assessent Fro the above analysis, a feature vector S can be defined, including the three aforeentioned signal characteristics that can be coputed at each tie bin for each uscle. The feature vector S i for each uscle i, i 1,..., 11, for the tie bin 1, 2,..., is defined by: S i IAV i ZC i V AR i 3 The tie bin spans fro tie 1NT to NT, where T the sapling period, i.e. T 1 sec. and N 100 the width of the tie bin. The purpose of the work, as described above, is to quantify in a sense the uscle fatigue, in order to be able to decide about the uscle condition and switch between different odels for EMG-based otion decoding. In other words, a easure of fatigue f i for each uscle i should be defined. Then, a set f i of possible fatigue states can be defined as shown below { } f i f i 1, fi 2,..., fi n 4 where n the nuber of fatigue states for the uscle i. Muscle fatigue is ainly caused by the repetitive force exertion of the uscle. Muscle force, as reported in the literature with the for of the well-known Hill uscle odel, is related to uscle length and uscle contraction velocity i.e. rate of change of the length 6]. These uscle characteristics are directly related to the angular position and velocity of the actuated joint through a siplified usculoskeletal odel of the ar. Fro the above, it is evident that the joint angle and the angular velocity should be incorporated in our analysis of uscle fatigue. This is because an increase at a signal characteristic e.g. the IAV i of the uscle i can be caused by large force exertion and not necessarily uscle fatigue. Muscle force can not be easily easured though. Therefore, its result, i.e. the angle and the angular velocity of the actuated joint, will be incorporated to the uscle fatigue analysis, a practice that is consistent to the concept of the aforeentioned odels. Moreover, since uscle actuate usually in ore than one DoFs, with the latter defined as in Fig. 2, the fatigue analysis of the 7 uscles of the shoulder i.e. deltoid anterior, deltoid posterior, deltoid iddle, pectoralis ajor, teres ajor, pectoralis ajor clavicular head and trapezius will incorporate the two DoFs of the shoulder, and respectively for the 4 uscles of the elbow i.e. biceps brachii, brachialis, brachioradialis and triceps brachii. Therefore, we can define a fatigue-related feature vector for each of the two uscle groups, i.e. F i ] T IAV i ZC i V AR i q 1 q 1 q 2 q 2, i 1,...,7, 1,..., the feature vector for the 7 uscles of the shoulder, and F i ] T IAV i ZC i V AR i q 3 q 3 q 4 q 4, i 8,...,11, 1,..., the feature vector for the 4 uscles of the elbow, coputed at each tie bin, while q 1, q 2, q 3, q 4 the joint angles at tie bin coputed by 1, and q 1, q 2, q 3, q 4 the respective angular velocities coputed through tie differentiation of the joint angles. In order to define the level of fatigue for the uscle i at each tie instance, according to the easured feature vector F i, we need to copute the conditional probability of the uscle being at the fatigue state f i, j 1,..., n, n the possible fatigue states, given the feature vector F i, i.e. Fi. This is done by using the Bayes theore 7], that in our case is described by the following equation. p F i f i Fi, j 1,...,n p F i 5 where p F i f i the probability density function PDF of the feature vector F i given the fatigue state f i, the prior probability of the fatigue state being f i and n p F i p F i f i 6 j1 the evidence factor that can be considered as a scale factor that guarantees the posterior probabilities su to one. The n fatigue states for each uscles i are considered equally likely to happen, i.e. P f i 1 P f i 2... P f i n 1 n 7

4 However the PDF of the feature vector F i given the fatigue state f i, p F i f i, the so-called likelihood ter, needs to be coputed. This is going to be achieved using the data collected through the training period. Since there is no specific relation between the coefficients of the feature vector, a flexible ethod of odeling will be used called Finite Mixture Models. Finite ixtures of distributions provide a atheaticalbased approach to the statistical odeling of a wide variety of rando phenoena 8]. In our case, where ore than one coponents i.e. features are to be odeled, that are not independent, a ultivariate ixture odel will be used. Moreover, a coon assuption in practice is to take the coponent densities to be Gaussian. Therefore, a ultivariate Gaussian Mixture Model GMM will be used for odeling the ultivariate density of the feature vector F i. Let F i the observed feature vector of uscle i at tie instance during the training procedure. The PDF of this can be odeled using a GMM that is defined by g p π h φ h F i, µ h,σ h 8 F i h1 where φ h F i, µ h,σ h represents a ultivariate Gaussian density function with µ h the ean vector, Σ h the respective covariance atrix, and π π 1... π g the vector of ixing proportions of the ixture, which su to one. Using the training data collected, the paraeters of the GMM, i.e. π, µ, Σ, are fitted using the Expectation Miniization EM algorith 8]. The nuber of the Gaussian coponents g is deterined by using the Akaike criterion, which is a widely-used easure of goodness of fit of an estiated statistical odel. In our case, the ixture coponents can be used for clustering the signal characteristics, into clusters that will represent essentially the fatigue level. This can be done once the ixture odels has been fitted, using a probabilistic clustering of the data into g clusters that can be obtained in ters of the fitted posterior probabilities of coponent ebership for the data. An outright assignent of the data into g clusters is achieved by assigning each data point to the coponent to which it has the highest posterior probability of belonging. Relating the fatigue level to the g clusters is feasible, since the ultivariate data odeled are selected to vary with the uscle fatigue level. Therefore, the set of fatigue levels defined in 4 for uscle i, can be redefined having g i states, i.e. { } f i f i 1, fi 2,..., fi g i 9 where g i the nuber of the coponents fitted to the data collected fro uscle i. Therefore, fro the aforeentioned analysis and after the training period, the uscle fatigue level can be assigned to each uscle i at each tie instance using 5. For each uscle i, the feature vector F i is coputed. Then for each of the fatigue levels j, j 1,..., g i, the conditional probability of the uscle being at the fatigue level f i can be coputed using 5, where p P p F i f i f i 1 F i gi P gi p j1 π h φ h F i, µ h,σ h... g i F i f i h1 f i 2 1 g i 10 Having coputed Fi for each fatigue level f i, j 1,...,g i, a decision about the fatigue level assignent to the uscle i can be ade, according to the siple Bayes decision rule, i.e. decide f i s if P f i s F i P f i h Fi, h 1,...,g i 11 where f s i the final fatigue assignent for uscle i. The above procedure is ipleented for all the recorded uscles, at each tie instance in real tie. During the training period, it was noticed that the EMG signal characteristics of each recorded uscle were varying isotropic. Due to this fact, the coponents g i for each uscle i were found to be equal in nuber aong the recorded uscles, while the switching aong the fatigue states, coputed fro 5, 10, 11, for each uscle was noticed to happen alost at the sae tie instance. This can be explained by the above reasons: Fatigue-related signal characteristics fro all uscles were varying isotropic during ar otion. Muscles usually act in synergies, therefore it s ore likely that they suffer fatigue in an approxiately synchronous anner. Ar otion perfored by the user covered ost of the ar kineatic workspace, in ters of joint configuration, and dynaic workspace in ters of joint velocity, activating all the recorded uscle isotropically and not wearing out only a subset of the. The decision for the global fatigue state f G is ade using the fatigue states of all the uscles, f s i, i 1,...,11, by deciding which of the states is ost popular aong the uscles. Let P h be the sets that include the uscles whose fatigue state is h, h 1,...,g. Thus, if Π the union of the sets P h, h 1,...,g, Π P 1 P2... P g 12 we have, Π 11 the total nuber of the population of the sets, which coincides with the nuber of uscles. If we denote an allocation rule r B f G for assigning the global fatigue state f G to one of the possible fatigue states, where r B f G f l iplies that the global fatigue state is assigned to the lth fatigue state l 1,...,g i, then the optial rule for the allocation of f G is defined by: r B f G arg axp h, where P h the population nuber of h the set P h, h 1,...,g. The above rule essentially eans

5 that the global fatigue state f G is the one that describes the fatigue state of the ajority of the recorded uscles. D. Fatigue-related Switching Decoder Since the nuber of uscles recorded is quite large i.e. 11, a low-diensional low-d representation of uscle activations will be used instead of individual activations. The ost widely used diension reduction technique is principal coponent analysis PCA. During the training period, the EMG recordings fro each uscle are preprocessed, i.e. full-wave rectified, low-pass filtered and noralized to their axiu voluntary isoetric contraction value 6]. Then they are represented into a low-diensional space, using the PCA algorith. It was found that a 2-diensional 2D space could represent ost the original high diensional data variance ore than %96. The authors have used the diensionality reduction for uscle activations in the past for planar oveents of the ar 9]. Therefore the details of the ethod application are oitted. Furtherore, the diensionality reduction technique will also be used for representing the ar otion in a low-diensional space, revealing otion priitives that are extensively discussed in the literature. Therefore, by using the PCA algorith the analyzed 4-DoF otion, described in joint angles i.e. q 1, q 2, q 3, q 4, is represented into a 2-diensional space. Indeed it was found that ost of the original data variance %97 was represented using a 2-diensional space. Having represented the uscle activations and the perfored joint kineatics into two low-diensional spaces, one can build a odel that will use the EMG lowdiensional ebeddings to estiate perfored otion. Let U t R 2 the 2-diensional vector of the low-diensional representation of the 11 uscle recordings, at tie t kt, k 1,.... Let y t R 2 be the low-diensional ebedding of the ar joint angles at the sae tie instance. The odel that will be used for decoding the EMG activity to perfored otion is defined as x t+1 Ax t + BU t + v t y t Cx t + υ t 13 where x t R d a hidden state vector, d the diension of this vector and v t, υ t zero-ean Gaussian noise in process and observation equations respectively, i.e v t N 0,W, υ t N 0,Q, where W R d, Q R 2 are the covariance atrices of v t, υ t respectively. Details about the odel structure and the fitting procedure can be found in 9]. A distinct odel of the for 13 is used for each of the g possible global fatigue states. Therefore, during training, data belonging to each one of the possible global fatigue levels are only used for the corresponding decoding odel. I.e. the odel h, h 1,...,g, is trained using data only when the global fatigue level is f h. During real-tie operation, the g trained odels are used to transfor the low-diensional ebeddings of uscle activations to low-diensional ebeddings of joint angles. The switching aong the odels is discrete, however, soothness in the transitions and the output odel estiations is Fig. 3. The block diagra of the proposed ethodology. q is the vector of the four joint angles decoded fro the EMG signals, while p d the pose vector coputed through the huan ar kineatics given the four joint angles. guaranteed since the initial hidden-state vector of a odel, iediately after a switching, is calculated through the observation equation of the odel previously used 1. In Fig. 3 the total architecture of the ethod for the real-tie otion decoding is depicted. E. Robot Control A 7 DoF anthropoorphic robot ar PA-10, Mitsubishi Heavy Industries is used. In order to control the robot ar using the desired joint angle vector q d 2, an inverse dynaic controller is used, defined by: τ Iq r q d + K v ė + K P e+g q r +C q r, q r q r +F fr q r 14 where τ τ 1 τ 2 τ 3 τ 4 is the vector of robot joint torques, q r q 1r q 2r q 3r q 4r the robot joint angles, K v and K p gain atrices and e the error vector between the desired and the robot joint angles, i.e. e q 1d q 1r q 2d q 2r q 3d q 3r q 4d q 4r 15 I, G, C and F fr are the inertia tensor, the gravity vector, the Coriolis-centrifugal atrix and the joint friction vector of the four actuated robot links and joints respectively, identified in 10]. The vector q d corresponds to desired angular acceleration vector that is coputed through siple differentiation of the desired joint angle vector q d q1d q 2d q 3d q 4d using a necessary low-pass filter to cut off high frequencies. More details about the controller can be found in 9]. III. RESULTS The proposed architecture is assessed through reote teleoperation of the robot ar using only EMG signals fro the 11 uscles as analyzed above. The robot ar used is a 7 DoF anthropoorphic anipulator PA-10, Mitsubishi Heavy Industries. The details of the experiental setup can be found in 11]. Real and estiated otion data were recorded for 3 inutes during the real-tie operation phase. The real joint angle 1 This is feasible since the C atrix of each odel has been defined as a full-rank atrix through the fitting procedure. 2 The vector of joint angles decoded fro EMG signals.

6 tested in a real-tie teleoperation task of a robot ar in the 3D space, lasted for about 3 inutes. It was shown fro the experiental results that the proposed ethod could estiate the huan ar otion using only EMG signals with high accuracy. The novelty of the ethod proposed here can be centered around two ain issues. First, the proposed ethod is not affected by EMG changes due to uscle fatigue. Since EMG is widely known as a non-stationary signal, the fact that the proposed ethod can copensate for EMG changes through tie ainly caused by uscle fatigue, is quite iportant for the field. The second iportant issue presented here is that, to the best of our knowledge, this is the first tie a continuous profile of 3D ar otion including 4 DoFs is extracted using only EMG signals. Most previous works extract only discrete inforation about otion, while there are soe works that estiate continuous ar otion, constrained though to isoetric oveents, single DoF, or very sooth otions 12]. ACKNOWLEDGMENT The authors want to acknowledge the contribution of the European Coission through contract NEUROBOTICS FP6-IST project. This research project is cofinanced by E.U.-European Social Fund 75% and the Greek Ministry of Developent-GSRT 25% through the PENED project of GSRT. Fig. 4. Real and estiated hand trajectory along the x, y, z axes, for a 3 inute period. Estiates fro the proposed switching ethod are quite close to the ground truth during the whole 3 inute test, while the stationary odel accuracy decreases after a period of approxiately 30 seconds. profiles were coputed fro the position tracker sensors, which were kept in place i.e. on the user s ar for offline validation reasons. The estiated user s hand 3D trajectory along with the ground truth are depicted in Fig. 4. As it can be seen the ethod could estiate the hand trajectory with high accuracy, copensating for EMG changes due to uscle fatigue. The latter is shown in Fig. 4, where the estiates based on a stationary decoding odel of the sae for of 13, that didn t copensate for uscle fatigue, are shown. As it can be seen, using a stationary odel, the accuracy of the estiates decreases with tie, due to uscle fatigue. IV. CONCLUSIONS AND DISCUSSION In this paper, a uscle fatigue-dependent ethodology for controlling an anthropoorphic robot ar using EMG signals fro the uscles of the upper lib, was proposed. A probabilistic fraework was designed in order to assign to each of the uscles recorded, a fatigue state. Then, a switching odel was built in such way to copensate EMG changes related to uscle fatigue. The proposed ethod was REFERENCES 1] O. Fukuda, T. Tsuji, M. Kaneko, and A. Otsuka, A huan-assisting anipulator teleoperated by eg signals and ar otions, IEEE Trans. on Robotics and Autoation, vol. 19, no. 2, pp , ] J. Zhao, Z. Xie, L. Jiang, H. Cai, H. Liu, and G. Hirzinger, Levenbergarquardt based neural network control for a five-fingered prosthetic hand, Proc. of IEEE Int. Conf. on Robotics and Autoation, pp , ] F. Tenore, A. Raos, A. Fahy, S. Acharya, R. Etienne-Cuings, and N. Thakor, Towards the control of individual fingers of a prosthetic hand using surface eg signals, Proc. 29th Annual International Conference of the IEEE EMBS, pp , ] R. H. Edwards, Huan uscle function and fatigue. huan uscle fatigue: physiological echaniss, Pitan Medical, London Ciba Foundation syposiu 82, pp. 1 18, ] R. Boostani and M. H. Moradi, Evaluation of the forear eg signal features for the control of a prosthetic hand, Physiol. Meas., vol. 24, pp , ] F. E. Zajac, Muscle and tendon: Properties, odels, scaling, and application to bioechanics and otor control, Bourne, J. R. ed. CRC Critical Rev. in Bioed. Eng., vol. 17, pp , ] R. O. Duda, P. E. Hart, and D. G. Stork, Pattern classification. John Wiley & Sons, Inc, ] G. McLachlan and D. Peel, Finite ixture odels. John Wiley & Sons, Inc, ] P. K. Arteiadis and K. J. Kyriakopoulos, Eg-based teleoperation of a robot ar using low-diensional representation, Proc. of IEEE/RSJ Int. Conf. Intelligent Robots and Systes, pp , ] N. A. Mpopos, P. K. Arteiadis, A. S. Oikonoopoulos, and K. J. Kyriakopoulos, Modeling, full identification and control of the itsubishi pa-10 robot ar, Proc. of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Switzerland, ] P. K. Arteiadis and K. J. Kyriakopoulos, Eg-based position and force control of a robot ar: Application to teleoperation and orthosis, Proc. of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Switzerland, ] Y. Koike and M. Kawato, Estiation of dynaic joint torques and trajectory foration fro surface electroyography signals using a neural network odel, Biol. Cybern, vol. 73, pp , 1995.