Extraction of Behavior Primitives for Understanding HumanStanding-up Motion

Qi AnDepartment of Precision Engineering

The University of Tokyoanqi@race.u-tokyo.ac.jp

Hiroki MatsuokaIHI Corporation

Yusuke IkemotoDepartment of Research into Artifacts, Center for Engineering

The University of Tokyo

Hajime AsamaDepartment of Research into Artifacts, Center for Engineering

The University of Tokyo

Abstract— Recently the aging society is very rapid, and it hasbrought many problems to our society. In order to avoid thesedifficult situations, we focus on human standing up motion inour research because this motion is so important to our dailylife that it is considered meaningful to support the motion.

However, the way of human standing up is still unknown be-cause the analysis of human motion is very difficult. Therefore,we develop integrated simulation methods to understandingthe motion from human body data, such as muscle activations(EMG) and human joint torques. We carefully analyze humanstanding up motion based on muscle movements since musclesdo move human body. Through our experiments and analysis,two important muscle coordinations (behavior primitives) arefound out; one primitive has a function of generating dynamicsof the motion by controlling hip, knee, and ankle and the otherprimitive controls posture of the body with their ankles. Thesebehavior primitives are elucidated to be such an essential factortoward the motion that the way of standing up becomes unstablewithout them.

Index Terms— Synergy, EMG, Torque Estimation, MotionTrajectory Estimation

I. I NTRODUCTION

A. Background

The aging society becomes very big issue especially indeveloped countries. While the population of younger peoplewill decline, changes in the population of elderly has beenvery rapid until now, and this trend seems to continue into thefuture[1]. The aging society has brought many problems toboth elder people and care givers. For example, QOL (Qualityof Life) is supposed to be decreased for those who arebedridden, and many care givers are suffered from physicalproblem such as backache since getting up people is a wearytask. Today, an idea of preventing nursing care is becomingmore and more important to avoid these problems. The ideasuggests that people should train by themselves for keepingthemselves healthy and in order not to rely on others.

In our research, human standing-up motion is considered tobe very important. Since many daily actions such as walking,shopping, or cleaning up their rooms, all start from standing-up motion, the motion should be regarded as an essential

motion for their daily life. Thus sufficient machines ormethods to train elderly people are really needed. However,the way how a person stands up is still unclear.

Human muscle coordinated movements are considered tobe important in our study because it is the fact that whena person moves, they have to use their several muscles.Also, since many elder people have some difficulties intheir motions due to weakened muscles, analysis based ontheir muscle strength is supposed to be very meaningful.Therefore, it is important to know how every muscle isactivated and what effect they have on the motion.

B. Objective

Through this study, our objective is to understand themechanism of human standing-up motion by extracting be-havior primitives which are muscle coordinated activationsand also consist human motion. In order to analyze thestanding-up motion, the integrated simulation method is de-veloped to elucidate the contribution of muscle coordinationstoward the actual motion. In this paper, we demonstrate thatthe motion can be divided into two main primitives: oneprimitive makes dynamics of the movement, and the othercontrols posture of the body.

II. M ETHODS FOREXTRACTION BEHAVIOR PRIMITIVES

A. Behavior Primitives

In our research, behavior primitives are defined as anelement which consists of human motion, and they arecoordination of several human muscles activation and eachprimitive has specific contribution toward the motion.

To illustrate the idea of muscle coordination, synergyhypothesis, which was suggested by Bernstein[3], is verysufficient. The hypothesis indicates that every human motioncan be divided into several muscles coordinations called asynergy and when a person actually moves, they coordinateeach synergy sufficiently.

To demonstrate an example of contribution of humanprimitive actions, proceeding study about a human bending

their trunk forward motion can be cited[7]. The researchrevealed that human bending forward motion consists oftwo parts; one is pulling their hip backward in order tomake dynamics of the motion, and the other is controllingtheir ankles in order to keep their posture stable. In theresearch, muscles coordinations are not considered, howeverthe functions of human actions are elucidated.

B. Model of Human Motion Generating

In order to extract human behavior primitives, it is nec-essary to understand the way how a person moves. Fig. 1shows a simple model of it.

First, motor commands are sent to human muscle froma human brain, and after their muscles receive signals tomove, each muscle generate a tension by extending orshrinking. Next, joint torques are generated by tensions ofmuscles attached to joints. Then, human body actually movesaccording to its kinematics.

Brain Muscle

Motor Control

Musculoskeletal

System

Generation of Tension Torques

Human Body

Movement

Fig. 1. Flow Chart of How a Human Moves

Although the model of human body movement can beindicated very simply, it is very difficult to express thoseprocesses accurately because there are many parameters to beputted for a human body and each parameter is very differentbetween individuals. In this paper, muscle EMG patterns areused for motor command from a brain, neural networks aresuitable for representing the relationship between musclesand torques, and a recurrent neural network is making amapping between torques and human body movement.

C. Synergy Analysis

1) Synergy Hypothesis:The synergy hypothesis was sug-gested by Bernstein in 1967[3]. Synergy is a group ofseveral muscles performing a coordinated movement. Wecan observe various patterns of muscle activity by surfaceelectromyography (EMG). The synergy hypothesis suggeststhat those observed muscle activities can be divided into fun-damental elements called synergy. Actually, d’Avella’s mod-eling of the synergy is efficient because their model suggeststhat muscle patterns can be generated as linear combinationsof time-varying synergy, which are time-varying profiles ofmuscle activity. Each synergy has intensity and onset delay.Synergies represent the time course of the activation levelfor each muscle. To generate the original muscle profiles,every i-th synergy must be scaled in amplitude by a non-negative coefficient (ci); every synergy is shifted in time byan onset delay (ti). Then the elements of different synergiesare summed together corresponding to the same muscle andsame time. Therefore, even though each synergy has its ownmuscle profile, it can regenerate muscle patterns of various

kinds by changing the amplitude and time delay[2]. Althoughd’Avella’s model is simple, it is an efficient way to describethe synergy hypothesis in a quantitative manner. In this study,we define synergies as human behavior primitives and extractthem.

2) Decomposition Algorithm:This algorithm which wasdeveloped by d’Avella[4].

In this model, let m(t) be a matrix representing activationof d muscles at a certain timet(0 < t ≤ tsynergy), and thesemuscles patterns are approximated by the linear-summationof time-varying synergy{wi(t)}|i=1...n (let n be the numberof synergies to be extracted) with non-negative coefficientci ,and onset delayti as in eq. (1).

m(t)∼= m′(t) =N

∑i=1

ciwi(t − ti) (1)

By the algorithm, every synergy patternwi(t), non-negativecoefficient ci , and onset delayti are obtained in order tominimize the total squared reconstruction errorE2 calculatedfrom eq. (2).

E2 = trace((Ms−WHs)

T(Ms−WHs))

(2)

3) Cross-Validation Method:In this synergy model, thenumber of synergies to extract is an important issue. Theaccuracy of the model must be tested in order to determinethe number[5]. If the number is smaller than the best fittednumber, the model cannot explain the observed data suffi-ciently; if it is beyond the best number, it is also not goodbecause the model extracts the specific data noise. Therefore,it is important to try the model using different numbers. Thecross-validation procedure is as follows.

First, twelve observed data are divided into four groups;each group has three datasets. Then three datasets are chosenfor training data and the other one dataset is for testingdata. Next, particula set of synergies is calculated fromthe chosen three datasets from the decomposition algorithm,and computed the mean validationR2 from eq. (3) withthe testing dataset.E2 is the squared error calculated fromeq. (2); S2

M is the variance of all observed EMG patterns.Repeat this process four times changing the test dataset toobtain the accuracy of the model for the particular numberof synergy. Doing this calculation for certain numbers, thespecific number is obtained.

R2 = 1− E2

S2M

(3)

D. Link Model

1) Human Body Model:Four links with three joints modelis used to represent the human body in this study becausethree joints, such as foot, knee, and hip, are only concerned. Each link indicates a particular human body part. Someassumptions are applied to this model.

1) Every link is rigid.2) Every joint is uniaxial; body movement is expressible

in the x-z plane.

ankleankle τθ ,

kneeknee τθ ,

hiphip τθ ,

ankle

articulatio

genus

great

trochanter

acrominon

iτ

jτ

mg

x jf

yjfx if

y if

),( ii yx

),( jj yx

),( nn yx

(a) (b)

Link1

Link2

Link4

Link3

0

x

z

Fig. 2. Link Model

(a) This figure portrays the positions measured by themotion capture machine: the ankle, knee, hip, and shoulder.

(b) This shows parameters being defined to every link.

3) The foot does not move.

2) Calculation of Torque:Floor reaction forces are mon-itored by using a force plate for computing joint torques.Forces and torques to the body are defined as shown inFig.2-(b), wherem is the mass of the body representedby a link, g is gravity acceleration,(xn,yn){n=1,2,3,4} isthe position of center of gravity of each link,fxi,x j is thehorizontal force of particular position,fyi,y j is the verticalforce,τi, j{i, j=ankle,knee,hip} is the torque of each joint,I is theinertial moment, andM is the moment from the center ofgravity. The equations of motion can be written as follows.

mxn = fx j − fxi (4)

myn = fy j − fyi −mg (5)

I θi = M− τi − τ j (6)

Those equations are approved to every linkn{n=1,2,3,4}.Therefore, these equations are solved for each torque byinverse calculation under the conditions of a link model.

E. Joint Torque Estimation

In this study, each human joint torque is estimated by everyneural network which was proposed by Koike[6]. Since jointtorques are generated from each tension of muscles whichare attached to the joints, muscle EMG patterns are putted asinputs of the network and torques are obtained as an outputsignals. There are ten hidden nodes for the network, andback-propagating rule is adopted for a learning rule. In orderto test the accuracy of the estimation,R2 from eq. (3) isused. When checking this, observed twelve data are dividedinto six training data which are only used for teaching thenetwork and six testing data which are used for calculatingaccuracy of the model.

F. Joint Angle Estimation

Human joint angles are also estimated by a neural network.For input signals, three joint torquesτi(t), joint anglesθi(t),and joint angular velocityθi(t) at t = t are putted (i =ankle,knee, and hip). Throughout fifteen nodes of a hidden layer,

∆θi(t + 1) and ∆θi(t +1) are obtained. For next inputs att = t +1, angleθi(t +1) and angular velocityθi(t +1) areadded by outputs∆θi(t +1) and∆θi(t +1).

In order to test the accuracy of the model, same methodfor torque estimation is used here.

G. Extraction of Behavior Primitives

1) Method of Checking The Contribution of BehaviorPrimitives: In this research, behavior primitives are definedas muscle coordinated movements, and in order to seecontributions of them, weakened EMG patterns, which arereconstructed by weakened synergies, are putted into theneural network model which estimates joint torque fromEMG patterns. The outputs of torque from neural networksshould be different from normal one because unusual patternsare used on purpose. Then, the recurrent neural network,which estimates human joint angles, receives changed inputsof joint torques. Therefore, this network outputs differentchange of angles and angular velocity according to alreadylearned nodes of the network.

To make methods clear, following procedures are used.1) Put weakened EMG patterns based on synergy patterns2) The first neural networks, which estimate joint torques

of human, give out changed torques simulated fromreal data.

3) The next recurrent neural network, which estimatejoint angles of human, receives unusual torques, andit outputs changed angle of human.

Three procedures are repeatedly used to simulate humanmotion from changed EMG patterns lacking particular syn-ergy.

Foot Torque Estimation

(Neural Network A)

Hip Torque Estimation

(Neural Network C)

Knee Torque Estimation

(Neural Network B)

footτ

kneeτ

hipτ

iθ∆

iθ•

∆

iθ•

iθ

+

+

Trajectory

Estimation

(Neural Network)

iEMG

iEMG

iEMG

Fig. 3. The Way of Figuring Out the Contributions of Behavior Primitives

2) Synergy Weakened Muscle Patterns:To complementthe method, it is necessary to explain how to generate inputsof EMG patterns by weakening particular synergy. To preparechanged patterns, it is needed to think of rates of contributionof each synergy; for example limiting synergy1 activation to50%. Although synergy model is very sufficient and usefulmethod, it cannot duplicate observed EMG patterns perfectly

due to observed data noise. Then, the rate of contributionsof each synergy is considered to make changed input data.

Suppose that one muscle activation level of synergy1 is0.6 and one of synergy2 is 0.2 at one certain time stept = T,and also acctual observed muscle activation is 1.0 whichis not equal to a linearly-summation of muscle activationsfrom synergy1 and synergy2. Then the contribution rateof synergy1 and synergy2 are decided to 75% and 25%since fraction of muscle activation from two synergies are3 : 1(0.6 : 0.2). In the example, trying to limit synergy1 to50%, it is needed to divide acctual observed value into 0.75and 0.25 first according to the ratio of each synergy. Then,muscle activation is weakened from 0.75 to 0.375, and justleave 0.25 remaind for synergy2. At last, their activations aresummed together again since synergy hypothesis suggests itis linearly-summation of different synergies.

III. E XPERIMENTAL SETUP

In the experiment we did, there are three main parts tomeasure.

1) Body Trajectory2) Floor Reaction Force3) Muscle EMG

These three parts are all important for the analysis of thehuman standing-up motion.

A. Measurement of Human Body Trajectory

Fig. 4-(a) shows the motion capture machine [HMK-200RT; MotionAnalysis], which is used in the experiment tomonitor the movement of the human while standing up. Therecorded parts are four points: acromion, greater trochanter,articulatio genus, and ankle as in Fig. 4-(b). Positions of thoseregions are necessary because they are endpoints of each link.Although the sampling rate was 64 Hz in this experiment,data are down-sampled to the 12.8 Hz when using this datafor computation, At the beginning of the standing-up motion,the subject keeps the angle of his ankle at 80 deg. His backwas straight; the chair height was 425 mm. Also, the subjectis asked to have his arms crossed in front of his chest toavoid the model becomes too complex by considering aninertia of arms. Those conditions were the initial state of thesubject. From this experiment, angle of each joint is obtained,θi{i=ankle,knee,hip} shown in Fig. 2-(a).

B. Measurement of Floor Reaction Force

Two force plates are used in this experiment. Each platemeasures the reaction force by the foot and hip of the subject.The figure of force plate is shown in Fig. 5. Same as motioncapture, although sampling rate of observed data is 64 Hz, itis down-sampled to 12.8 Hz when used.

Fig. 4. Motion Capture Machine and Markers Position

(a) The motion capture machine[HMK-200RT;MotionAnalysis] (b) Positions measured by the motioncapture machine: the ankle, articulatio genus, greater

trochanter, and acromion.

Fig. 5. Force Plates

C. Measurement of EMG

One healthy 22-years-old man participated in this experi-ment. To analyze EMG signals while standing up, they arerecorded from eight muscles, as presented in Fig.6. Thosemuscles are considered important for standing-up motionfrom an anatomic viewpoint because every observed muscleis supposed to be related to inflection of three concernedjoints. The EMG data are filtered with an upper cut-offfrequency of 500 Hz and lower cut-off frequency of 200Hz. Twelve trial data are obtained from this experiment.In addition, those data are filtered using a smoothing filterand down-sampled these data sampling rates of 12.8 Hzfrom 11200 Hz. Additionally, muscle data are normalizedas 0–1 using the benchmark in maximum muscle activity forall trials. The EMG patterns obtained from this experimentwere eight (four muscles for each half of the body), yetthe function of muscles of the whole body is regarded asequivalent. Therefore, the values of the EMG patterns areaveraged from the same muscle.

Musculus

Quadriceps

Femoris

Musculus

Latissimus

Dorsi

Musculus

Gastrocnemius

Musculus

Tibialis

Anterior

Fig. 6. This figure shows EMG sensor locations; the gastrocnemius muscle,quadriceps femoris muscle, gluteus muscle, latissimus dorsi muscle, and theprevertebral muscle.

IV. A NALYSIS OF HUMAN STANDING-UP MOTION

A. Extraction of Synergies

The number of synergies to be extracted from the observedEMG patterns is clarified by cross-validation. The relation-ship between mean value ofR2 and the synergy number isdepicted in Fig.7.

Specifically regarding synergy number three, it is a suf-ficient number: before that number, the slope of the graphincreases rapidly; after that point, the slope does not changesharply.

It seems that the number of synergies to be extracted isthree from the result, however one of the synergies does notinclude any activated muscles and its contribution toward thebody is rather small. This synergy is supposed only to workas removing specific small noise of patterns.

Fig.8 indicates acctual extracted two synergies. In syn-ergy1, every four muscles are activated and there are onlytwo muscles are active in synergy2, such as musculus gas-trocnemius and musculus latissimus dorsi.

0.0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5

The Number of Synergy

Cross Validation Method Result

for Subject A

R2

Fig. 7. A Result of Cross Validation Method for Subject A

B. Estimation Results of Joint Torques and Angles

Fig.9 (a) shows one example of torque estimation byneural networks. The model of generating torques by severalmuscles is very accurately indicates really observed torques.In order to evaluate the accuracy of the model, equation (3)is used. The results are shown in Table.I.

Fig.9 (b) is one of the examples of comparing the estimatedangles and acctual observed angles. Table.II also indicateshigh score onR2.

These results suggest the reliability of the model for bothtorque and angle estimation.

TABLE I

TORQUEESTIMATION RESULTS

AverageR2 Standard DeviationFoot Torque 0.916 0.088Knee Torque 0.933 0.024Hip Torque 0.954 0.012

0.0

0.2

0.4

0.6

0.8

1.0

1 6 11 16

Mus

cle

Act

ivat

i

Time Step

Musculus Tibialis Anterior

0.0

0.2

0.4

0.6

0.8

1.0

1 6 11 16

Mus

cle

Act

ivat

i

Time Step

Musculus Quadriceps Femoris

0.0

0.2

0.4

0.6

0.8

1.0

1 6 11 16

Mus

cle

Act

ivat

i

Time Step

Musculus Gastrocnemius

0.0

0.2

0.4

0.6

0.8

1.0

1 6 11 16

Mus

cle

Act

ivat

ion

Time Step

Musculus Latissimus Dorsi

0.0

0.2

0.4

0.6

0.8

1.0

1 6 11 16

Mus

cle

Act

ivat

i

Time Step

Musculus Tibialis Anterior

0.0

0.2

0.4

0.6

0.8

1.0

1 6 11 16

Mus

cle

Act

ivat

i

Time Step

Musculus Quadriceps Femoris

0.0

0.2

0.4

0.6

0.8

1.0

1 6 11 16

Mus

cle

Act

ivat

i

Time Step

Musculus Gastrocnemius

0.0

0.2

0.4

0.6

0.8

1.0

1 6 11 16

Mus

cle

Act

ivat

i

Time Step

Musculus Latissimus Dorsi

Synergy1 Synergy2

Fig. 8. Extracted Two Synergies

1.2

1.3

1.4

1.5

1 11 21 31

Foo

t Ang

le

Time Step

Foot Angle Estimation Result for Subject A

Estimated Line

Observed Line

1.5

1.8

2.1

2.4

2.7

3.0

1 11 21 31

Kne

e A

ngle

Time Step

Knee Angle Estimation Result for Subject A

Estimated LineObserved Line

0.8

1.0

1.2

1.4

1.6

1 11 21 31

Hip

Ang

le

Time Step

Hip Angle Estimation Result for Subject A

Estimated LineObserved Line

[rad]

[rad]

[rad]

0.0

0.2

0.4

0.6

0.8

1.0

1 11 21 31

Foo

t Tor

qu

e

Time Step

Foot Torque Estimation Result for Subject A

Estimated Line

Observed Line

0.0

0.2

0.4

0.6

0.8

1.0

1 11 21 31

Kne

e T

orqu

e

Time Step

Knee Torque Estimation Result for Subject A

Estimated Line

Observed Line

0.0

0.2

0.4

0.6

0.8

1.0

1 11 21 31

Hip

Tor

que

Time Step

Hip Torque Estimation Result for Subject A

Estimated Line

Observed Line

(a) (b)

Fig. 9. Angle Estimation Results for Subject A

C. Contribution of Behavior Primitive

Fig.10 shows error value calculated by formation (7) whereθdop(t) is observed angle for each joint angle andθest(t) isestimated joint angle. Error values are normalized accordingto max error of each joint angle in order to understandcontribution of the model easily.

Ei= f oot,knee,hip =t

∑t=1

|θdop(t)−θest(t)|i (7)

As limitation toward each synergy is increased, errorvalues are also increased. In addition, errors of knee,and hipsuddenly increase rapidly at 30% point.

While normal standing motion lets knee go straight up-ward, the simulated angle line shows knee angle of weakened

TABLE II

ANGLE ESTIMATION RESULTS

AverageR2 Standard DeviationFoot Angle 0.841 0.098Knee Angle 0.994 0.005Hip Angle 0.948 0.075

synergy1 model does not go straight as much as normal one.The angle of their foot is also changed rapidly compared tonormal one.

Thus, this synergy1 is supposed to make large movementof the motion, such as returning their bended back, or liftingtheir upper body upward by their knee in order to carry theircenter of gravity forward.

On the other hand, synergy2 works only for controllinghuman foot because as more limitation putted on the synergy,more errors are occurred only to foot angle. Synergy2 can bethought to control human posture because it starts at middleof the motion. At that moment people easily become unstablebecause they have to move their center of gravity from hipto their foot. Synergy2 mainly works for compensation ofmovement of center of gravity. In the contrast, Fig. 10 and11 imply that synergy 2 has less effect on knee and hip thansynergy1.

0.0

0.2

0.4

0.6

0.8

1.0

90% 80% 70% 60% 50% 40% 30% 20% 10%

Erorr

Percent of Limitation of Synergy1

Synergy1 Contribution to Error

footkneehip

0.0

0.2

0.4

0.6

0.8

1.0

90% 80% 70% 60% 50% 40% 30% 20% 10%

Ero

rr

Percent of Limitaion of Synergy2

Synergy2 Contribution to Error

footkneehip

Fig. 10. Contribution of Each Synergy to Joint Angle

V. CONCLUSION

Human complex musculoskeletal system is expressed suffi-ciently in this paper. It constructs a mapping between humanmuscles and their joint toques, and between joint torques andhuman body trajectory. Using this integrated analysis method,a contribution of several muscle movements toward a motionis elucidated.

In addition, the synergy analysis is applied to human-standing up motion, and sufficient two important musclecoordinations are extracted. From the model, it is clearthat both two coordinated muscle patterns have significantfunction to their movement. One behavior primitive works formaking dynamics of the body by moving their ankle, knee,and hip. The other controls their ankle in order to keep theirposture stable. Even when a person lacks either of behaviorprimitives, the motion is obviously changed and they cannotstand up.

(a) (b)

1.1

1.2

1.3

1.4

1.5

1 11 21 31

An

gle

Time Step

Foot Angle

Normal

70%

40%

30%

20%

10%

1.5

1.8

2.1

2.4

2.7

3.0

1 11 21 31

An

gle

Time Step

Knee Angle

Normal

70%

40%

30%

20%

10%

0.8

1.0

1.2

1.4

1.6

1 11 21 31

An

gle

Time Step

Hip Angle

Normal

70%

40%

30%

20%

10%

1.1

1.2

1.3

1.4

1.5

1 11 21 31

An

gle

Time Step

Foot Angle

Normal

70%

40%

30%

20%

10%

1.5

1.8

2.1

2.4

2.7

3.0

1 11 21 31

An

gle

Time Step

Knee Angle

Normal

70%

40%

30%

20%

10%

0.8

1.0

1.2

1.4

1.6

1 11 21 31

An

gle

Time Step

Hip Angle

Normal

70%

40%

30%

20%

10%

Fig. 11. Angle Changes with Weakened Particular Synergy

(a) angle changes with weakened synergy1(b) angle changes with weakened synergy2

VI. D ISCUSSION ANDFUTURE WORKS

Although we are able to extract two sufficient behaviorprimitives and check their contributions in this paper, it isstill unknown whether these behavior primitives are commonto every person. It is very important to see if this developedsimulation method is also useful to other people.

Furthermore, in order to achieve our goal, which preventselder people from needing a nursing care, new trainingmachines or methods should be developed. From the resultsobtained in this research, two ways of muscle coordinationsare observed, and since both of two has important contribu-tions, we are going to think of new methods to enhance thesebehavior primitives.

ACKNOWLEDGMENT

We thank Mr. Okamoto for help in constructing our experi-mental machines, and also thank Prof. Kandou Kobayashi forgiving us experimental opportunities.

REFERENCES

[1] Department of Economic United Nation and Social Affairs. Worldpopulation. pp 1-2, 2006

[2] d’Avella, Andrea et al., ”Combination of muscle synergies in theconstruction of a natural motor behavior,” Nature Neuroscience vol. 6no. 3 March 2003.

[3] Bernstein, Nicholai A. The Co-ordination and Regulation of MovementPergamon, Oxford, 1967

[4] Andrea d’Avella, Decomposition of emg patterns as combinations oftime-varying muscle synergies,IEEE EMBS Conference on NeuralEngineering, 2003, pp 44-48.

[5] Bishop, C. Neural Networks for Pattern Recognition,Clarendon, Ox-ford, UK, 1995

[6] Koike, Yasuharu et al., Estimation of dynamic joint torques and trajec-tory formation from surface electromyography signals using a neuralnetwork model,Biol. Cybern. vol. 73 291-300, 1995.

[7] A.V.Alexandrov, A.A.Frolov, and J.Massion.,Biomechanical analysis ofmovement strategies in human forward trunk bending. II.Experimentalstudy,Biol. Cybern.. vol. 84 435-443, 2001.