2012 IEEE/RSJ International Conference onIntelligent Robots and Systems
October 7-12, 2012. Vilamoura, Algarve, Portugal

Iterative Learning Control for a Musculoskeletal Arm:
Utilizing Multiple Space Variables to Improve the Robustness
Kenji Tahara, Yuta Kuboyama and Ryo Kurazume
Abstract— In this paper, a new iterative learning control method which uses multiple space variables for a
musculoskeletal-like arm system is proposed to improve therobustness against noises being included in sensory information.
In our previous works, the iterative learning control method forthe redundant musculoskeletal arm to acquire a desired endpoint trajectory simultaneous with an adequate internal force
was proposed. The controller was designed using only muscle
space variables, such as a muscle length and contractile velocity.
It is known that the movement of the musculoskeletal system
can be expressed in a hierarchical three-layered space whichis composed of the muscle space, the joint space and the task
space. Thus, the new iterative learning control input is composed of multiple space variables to improve its performanceand robustness. Numerical simulations are conducted and theirresult is evaluated from the viewpoint of the robustness to noises
of sensory information. An experiment is performed using a
prototype of musculoskeletal-like manipulator, and the practicalusefulness of the proposed method is demonstrated through theresult.

I. INTRODUCTION
There is no doubt that human’s natural movements arestill more smooth, dexterous and sophisticated than present
robotic systems. Recently, the realization of robots that behave smoothly and softly as with humans is highly expected
in order to help us in our daily life. Particularly, modelingof a control strategy of human body movements is quite
valuable for robots operated around our living space in thisregard. It is well-known in physiological and kinesiologicalfields that the human’s natural movements are performed byan adequate combination of a sensory feedback manner using
several external sensors such as a vision or tactile sensor
and a feed-forward manner obtained through sophisticatedlearning and estimation strategies [1], [2]. Thus, not only
how to design both the feedback and feed-forward control
strategies, but also how to merge them adequately is important to acquire the human’s natural movements.
Meanwhile, it is well-known in robotics field that an
iterative learning control method is quite effective for robots
to acquire a desired time-dependent movement [3], [4]. Thismethod is composed of a feedback manner and a feedforward manner similar to the human’s control strategy.
Before learning, the control input is composed only of theK. Tahara is with Faculty of Engineering, Kyushu University, 744
Moto’oka, Nishi-ku, Fukuoka 819-0395, Japan. tahara@ieee.org
Y. Kuboyama is with Graduate School of Information Science and Electrical Engineering, Kyushu University, 744 Moto’oka, Nishi-ku, Fukuoka
819-0395, Japan. kuboyama@irvs.ait.kyushu-u.ac.jp
R. Kurazume is with Faculty of Information Science and ElectricalEngineering, Kyushu university, 744 Moto’oka, Nishi-ku, Fukuoka 8190395, Japan. kurazume@ait.kyushu-u.ac.jp

978-1-4673-1735-1/12/S31.00 ©2012 IEEE

feedback manner, and then the control signal gradually governed by the feed-forward manner according to the increaseof the number of trials. Eventually, the control input is mostly
composed of the feed-forward control manner after learning
well through several trials. The method is quite robust tomodeling errors and unknown parameters.
Until now, we have utilized the iterative learning control
scheme to a musculoskeletal arm model whose muscle
model owns a strong nonlinear characteristics [5], [6]. A
desired time-dependent end-point trajectory with an adequate
internal force can be obtained by using the proposed method.
In the previous works, the desired time-dependent trajectory
was designed in the task space, and the control signal was
designed in the muscle length space by computing inverse
kinematics from the task space to the muscle space. Thus,
the controller consisted only of the muscle space variables,such as a length and contractile velocity of the muscle.
Meanwhile, the movement of the musculoskeletal system canbe expressed not only in the muscle space, but also the joint
space, or the task space. These spaces make a three-layered
structure, and the dynamics of the system and its controller
can also be expressed in each space. The performance of thecontroller partially depends on which space the controller
is designed in, and thereby it is important and valuable todiscuss which space is better to design the controller. Additionally, it is inevitable that sensory information includes
noises. For instance, it is known that the muscle information,
which can be measured as EEG, includes a lot of noises.
Since the kind of included noises is different in each space,
their effect to the movement is also different. There is apossibility to be able to improve the learning controller tobe robust to these noises by using plural space variables inthis regard.
In this study, a new iterative learning control method is
proposed which utilizes plural space variables to improve
its performance and robustness against noises. The iterative
learning control input is basically composed of a linear
summation of a sensory feedback part and a feed-forward
part obtained through the iterative learning process. The
proposed control input utilizes different space variables tocompose the feedback part and the feed-forward part to berobust to these noises. In what follows, firstly a two-link sixmuscle musculoskeletal planar arm is modeled in Section II.
Secondly, a nonlinear muscle model based on a physiologicalstudy is presented in Section III. Next, the validity ofthe proposed controller is shown by numerical simulation
results in Section IV. Finally, the practical usefulness of the
proposed controller is demonstrated through an experimental

4620

The relation between the vector of the muscular force
f m = [fm1 , fm2 , · · · , fm6 ]T ∈ R6 which depends on acontrol signal to be designed in the next section, and thevector of the joint torque τ = [τ1 , τ2 ]T ∈ R2 is given by theprinciple of virtual work in the following manner:(x,y)τ = W f m ∈ R2 ,Assume that W ∈ R2×6 is of row full-rank during movement, and then the inverse relation of (3) is given as follows:(4)f m = W + τ + I 6 − W + W k ∈ R6 ,

q2

l5
y

where W + = W T (W W T )−1 ∈ R6×2 , I 6 ∈ R6×6 denotes
an unit matrix, and k ∈ R6 denotes an arbitrary vector. The
physical meaning of the second term of the right-hand side of(4) is an internal force space which is generated by redundantmuscles. In addition, the statics between τ and the vector of
the output force of the end-point in the task space F ∈ R2
is given as follows:

l6

l3

l4
l2

l1

q1

τ = J T F ∈ R2 .

x

Fig. 1.

result in Section V.
II. T WO -L INK S IX -M USCLE M USCULOSKELETAL A RM
M ODEL
Figure 1 shows a musculoskeletal arm model used in thisstudy. The model is composed of two rigid links and fourmono-articular muscles and two bi-articular muscles. Thisis a planar arm and then its movement is limited within ahorizontal plane. Therefore the gravity effect is ignored. Eachmuscle is approximated as a linear segment, and assumingthat the mass of the muscles is included into the mass of eachlink. Note that the mesurable variables are the position of theend-point and its velocity a visual sensor, and each muscle
length and its contractile velocity by an encoder instead ofa muscle spindle.
A. Kinematics
The forward kinematics from the joint angle to the muscle
length is given as follows:
T

(1)

6

where l = [l1 , l2 , · · · , l6 ] ∈ R denotes the vector of themuscle length, q = [q1 , q2 ]T ∈ R2 denotes the vector of thejoint angle. Also, Gl (q) in (1) is a nonlinear vector functionthat expresses the relation between each joint angle and eachmuscle length. The time derivertive of (1) is given as follows:l̇ = W T q̇ ∈ R6 ,(5)

where J ∈ R2×2 denotes the Jacobian matrix for the endpoint velocity with respect to each joint angular velocity.
Substituting (5) into (4) yields:(6)f m = W + J T F + I 6 − W + W k ∈ R6 .

Two-link six-muscle musculoskeletal arm modell = Gl (q) ∈ R6 ,(3)

Equation (6) shows the inverse relation of the statics between
f m and F . Meanwhile, the forward kinematics from the joint
angle q ∈ R2 to the end-point position in the task spacex ∈ R2 is given as follows:
x = Gx (q) ∈ R2 ,where Gx (q) is a nonlinear vector function that expresses
the forward kinematics from the joint angle to the end-point
position. The time derivertive of (7) is given as follows:ẋ = J q̇ ∈ R2 .

(8)

Assume that J is of full-rank, thus the inverse relation of(7) and (8) can be given in the following way:2
q = G−1
x (x) ∈ R

q̇ = J−12ẋ ∈ R ,(9)(10)

where G−1
x (x) denotes a nonlinear vector function whichmeans the inverse kinematics from the end-point position to
the joint angle. Also, (10) denotes the differential inverse
kinematics from the end-point velocity to the joint angularvelocity. Substituting (9) into (1), and (10) into (2), respectively, yields


6
(11)
l = Gl G−1
x (x) ∈ Rl̇ = W T J −1 ẋ ∈ R6 .

(2)

where W T ∈ R6×2 is the Jacobian matrix for each muscle
contractile velocity with respect to each joint angular velocity, and it is called “the muscle Jacobian matrix” hereinafter.

(7)

(12)

Equations (11) and (12) show the inverse kinematics fromthe task space to the muscle space, and these are utilized in
the feed-forward manner.

4621

B. Nonlinear Muscle Model
A modified Hill’s muscle model has been utilized in ourprevious works [5], [6]. It can express a nonlinearity of theskeletal muscle with respect to the muscle contractile velocity. However, it does not consider any nonlinear elasticity inwhich the skeletal muscle intrinsically owns. In this study,
another nonlinear muscle model is newly modeled based on
the Audu’s model [7]. The Audu’s model consists of two
independent parts, an active contractile element dependingon the muscle activation level, and a passive nonlinear elastic
element. Since Audu’s model considers only a static situationand there is no effect of the muscle contractile velocity,
both active and passive viscous elements are newly added to
the Audu’s model in this study. The active viscous element
depends on the muscle activation level, and the passive
viscous element is a constant. Basically, both the viscouselements have been modeled as a part of our previously
proposed model. Namely, the new muscle model includes
Audu’s model and a part of our previous model. It is isgiven as follows:
˙ = u − p1 ep2 (l−l0 ) − (c1 u + c2 )l,˙
fm (u, l, l)(13)

˙ is the muscle output force, u signifies thewhere fm (u, l, l)
control input to the muscle, l stands for the length of themuscle, l0 indicates the intrinsic rest length of the muscle,l˙ denotes the contractoin velocity of the muscle, p1 , p2 , c1
and c2 are a positive constant, respectively. Namely, the firstterm of the RHS indicates the active contractile element, thesecond term of the RHS indicates a passive nonlinear elastic
element, and the last term of the RHS indicates both theactive and passive viscous elements which are newly added
to Audu’s model.
III. I TERATIVE L EARNING C ONTROL L AW
The PI-type iterative learning control method [8] is introduced to accomplish a given desired time-dependent trajectory. Time series error datasets regarding position andvelocity are stored during one trial to compose an input for
the next trial. The datasets are multiplied by the learning
gains, and added to the control input for the next trial.
As mentioned in Section I, there are three candidatesof state space to compose the iterative learning control
input, which are the muscle space, the joint space, and thetask space. Therefore, which spaces are better to compose
the control input is quite important to obtain a desirable
performance. In addition, it is inevitable that some noises areincluded into sensory information, and they strongly affectthe movement of musculoskeletal system. Several different
types of noises are included into the sensory information
obtained from each space. Therefore, the robustness to thenoises are also different according to which spaces thecontroller is designed in. In order to improve the robustness
to the noises included into the sensory information, a newiterative learning control method is proposed which utilizes
plural state space variables. In this paper, the task space ischosen to design the feedback manner, and the muscle spaceis chosen to design the feed-forward manner as one of thecase studies. The control input to the muscles at the ith trial
is given as follows:
J T (K p Δxi − K v Δẋi )ui = − W +
 i i +
+ I 6 − W i W i + vi ,(14)

where the subscript i indicates the trial number, K p =diag[kp1 , kp2 ] ∈ R2×2 > 0 denotes the task space position
feedback gain, K v = diag[kv1 , kv2 ] ∈ R2×2 > 0 signifies
the task space velocity feedback gain, and v i is the feedforward term obtained through the iterative learning process.
The position and velocity errors in the task space are given
as Δxi = xi − xd ∈ R2 and Δẋi = ẋi − ẋd ∈ R2 where
xd and ẋd are the desired time-dependent end-point positionand velocity trajectories in the task space, respectively. The
feed-forward term v i ∈ R6 is designed not in the task space
similar to the feedback manner, but in the muscle space, and
it is updated in the following manner:0 if i = 1 ,vi =if i > 1(1 − β) v i−1 − ΦΔli−1 + ΨΔl̇i−1(15)where Φ = diag[φ1 , φ1 , · · · , φ6 ] ∈ R6×6 > 0 and Ψ =diag[ψ1 , ψ2 , · · · , ψ6 ] ∈ R6×6 > 0 are the position andvelocity learning gain matrices, respectively. The positionand velocity errors in the muscle space are given as Δli =li − ld ∈ R2 and Δl̇ = l̇i − l̇d ∈ R2 where ld ∈ R6 and l̇d ∈R6 are the desired muscle length and contractile velocity
associated with the given desired time-dependent end-point
position and velocity trajectories in the task space xd andẋd . They are given by computing the inverse kinematics inthe following way:

 −1


(16)
Δli = Gl G−1
x (xi ) − Gl Gx (xd ) ,−1
Δl̇i = W Ti J i Δẋi .

(17)

The noises included into the sensory information are assumed to be Gaussian noise in this study. It is known that anerror of the initial condition between each iterative trial, anda fluctuation of the dynamics regarding some noises make theoverall system unstable when utilizing the iterative learning
control method. In order to overcome the effect of the noises,
Arimoto [9] has introduced a forgetting factor in the iterative
update law. Using the forgetting factor guarantees that the
final convergence trajectory of the system after learning wellis on the vicinity of the desired trajectory. In (15), β denotes
the forgetting factor, and it must be chosen so as to satisfy
0 < β < 1. Assume that the sensory information of themuscle length and the end-point position, and their eachvelocity independently includes Gaussian noise, respectively.
The magnitude of the noise for the end-point position andvelocity in the task space is assumed to be up to 4% of
the actual information, and that for the muscle length andcontractile velocity is assumed to be up to 50% of the actual
information. This is because we assume that the end-point
position and velocity are measured by eyes whose obtaind

4622

TABLE I
P HYSICAL PARAMETERS OF THE TWO - LINK SIX - MUSCLE ARM MODEL

1st Link
2nd Link

Length
[m]
0.31
0.34

Mass
[kg]
1.93
1.52

Inertial moment[kg·m2 ]0.0141
0.188

TABLE IIIG AINS

CoM position
[m]
0.165
0.17

Feedback Gain
Learning Gain

Ktp = 30I 2
Φm = 160I6

K tv = 20I 2
Ψ = 200I 6

5

Muscle space only
Task space only
Task & Muscle

TABLE II4

Muscle
f1
f2
f3
f4
f5
f6

l0 [m]
0.1
0.055
0.34
0.25
0.2
0.17

p1
4.0
4.0
4.0
4.0
4.0
4.0

p2
15.0
15.0
15.0
15.0
15.0
15.0

c1
10.0
10.0
10.0
10.0
10.0
10.0

Integral error

M USCLE PARAMETERS
c2
100.0
100.0
100.0
100.0
100.0
100.0

3
2
1

information is relatively accurate, and the muscle length andcontractile velocity are measured by a muscle spindle whose
obtained information includes a large electrical noise.
IV. N UMERICAL S IMULATIONS
Numerical simulation results are shown here to verify therobustness of the proposed controller. Each physical parameter and gain is shown in Table I to III. The desired timedependent trajectory is designed subject to the minimum
jerk criterion proposed by Flash and Hogan [10], which
minimizes the following performance index C.
 T...
 x(t)2 dt,
(18)
C=
0

...
where T is a duration time of the movement, and x stands
for a jerk of the end-point in the task space. Note that theminimum jerk criterion is used in the simulation as oneof the case studies, and any other physiological hypotheses
can be utilized instead of the minimum jerk criterion. The
desired trajectory is designed as a circle in the task space.
By calculating (18), it is given as follows: t 

−R
R cos 2πω
T 

∈ R2
(19)
xd (t) = x0 +R sin 2πω Tt
 5
 4
 3
 
(20)
ω Tt = 6 Tt − 15 Tt + 10 Tt ,where x0 denotes the initial position and is set to be[−0.02, 0.46]T , and R denotes the radius of the circle and is
set to be 0.1 [m]. The duration time T is set to be 1 [s].
In order to show the advantage of the new controller,
three types of numerical simulations are conducted. One
is using the proposed controller that is composed of boththe task and muscle space variables. The others are using
a conventional iterative learning controller that is composedof either the task space or the muscle space variables. As
mentioned in Section III, in all the simulations, each endpoint position and velocity information includes Gaussian
noise whose magnitude is up to 4% of the actual information,and each muscle length and contractile velocity information
includes Gaussian noise whose magnitude is up to 50% of
the actual information.

0
0

200

400

600

800

1000

Trial Number
Fig. 5. History of integral square errors of the end-point position according
to the number of trials: using both the task and muscle space variables, using
only the task space variables, and using only the muscle space variables

Figure 2 shows the loci of the end-point position in thecase of using the new controller. Figures 3 and 4 show
the loci of the end-point position when the controller isdesigned using either the task space or the muscle spacevariables, respectively. We see from these figures that theend-point position trajectory in all cases mostly converges
to the vicinity of the desired one according to the increaseof the number of trials. Clearly, the performance of the newly
proposed controller is better than that of other conventional
iterative learning control methods.
Figure 5 shows the history of integral square errors of
the end-point position according to the number of trials ineach simulation. We see from the figure that the integral
square error gradually diverges according to the increase of
the number of trials when using only the task space variables.
Meanwhile, the error increases and decreases intensely andits amplitude is relatively large when using only the muscle
space variables, although it does not diverge unlike that ofusing only the task space variables. In contrast, clearly the
integral square error is smaller than that of other cases in thecase of using the new controller. Thus, it is confirmed that theperformance of the new iterative learning controller is better
than other conventional iterative learning controller, eventhough the sensory information includes Gaussian noises,
particularly, the sensory information of the muscle spacevariables includes up to 50% of the actual information.
V. E XPERIMENT
An experimental result is shown here to demonstrate thepractical usefulness of the proposed controller. A two-link
six-muscle wire-driven planar arm developed in the study
is shown in Fig. 6 Six wires, which are made of Kevlar
produced by DuPont, are utilized to mimic the muscle-like

4623

0.55

0.45

0.6

Desired
1st
th
10
th
100
th
1000

0.55
0.5
y [m]

0.5
y [m]

0.6

Desired
st
1
10th
th
100
th
1000

0.45

0.5
0.45

0.4

0.4

0.4

0.35

0.35

0.35

−0.25

−0.2

−0.15

−0.1
x [m]

0

−0.05

−0.25

Fig. 2. Loci of the end-point position when thecontroller is designed using both the muscle andtask space variables

−0.2

−0.15

−0.1
x [m]

−0.05

0

−0.25

Fig. 3. Loci of the end-point position when thecontroller is designed using only the task spacevariables

Desired
1st
th
10
th
100
th
1000

0.55

y [m]

0.6

−0.2

−0.15

−0.1
x [m]

−0.05

0

Fig. 4. Loci of the end-point position when thecontroller is designed using only the task spacevariables

CCD Camera

2-link 6-muscle Planar Arm
Fig. 6. Experimental setup of the two-link six-muscle wire-driven planararm system
TABLE IV
P HYSICAL PRAMETERS OF THE EXPERIMENTAL SETUP

1st Link
2nd Link

Length
[m]
0.21
0.23

Mass
[kg]
0.97
0.03

Inertial moment[kg·m2 ]
0.063
0.001

CoM position
[m]
0.05
0.08

driven mechanism. They are connected to each link and six
DC-motors through several pulleys. Each physical parameterof the system is shown in Table IV. The actuators areproduced by FAULHABER which each has a 1:13 ratio gearhead and a rotary encoder. The CCD camera to measure theposition of the end-point in the task space is Dragonfly2
which can capture a visual image in every 33 [ms]. The
overhead view of the experimental setup is shown in Fig. 7.
In order to show the performance of the new controller forvarious kinds of desired trajectories, the desired end-point
trajectory in the experiment is designed as a linear segmentthat is different from the simulation. It is given as follows: (21)
xd (t) = x0 + (xf − x) ω Tt
where x0 ∈ R2 is the initial position, xf ∈ R2 is the final
position of the end-point respectively, and ω has alreadyshown in (20). The concrete value of each x0 , xf andFig. 7.

Overhead view of the experimental setup

the loci of the desired trajectory are shown in Fig. 8 The
duration time T is set to be 3 [s]. In the experiment, thenonlinear muscle model is computationally implemented asa soft-ware. In order to save substantial time, a numericalsimulation of the iterative learning in a thousand times
trials is performed, and finally acquired control input by
the simulation is utilized as the initial control input for theexperiment before performing the experiment. The iterative
trial number is ten times in the experiment.

4624

Initial Positionx0 = [148.5, 378.5]Tdynamics, the noises and such time-delay.

Final Position
xf = [-320.0, 101.0]T

Fig. 8.

Desired trajectory of the end-point in the task space

0.5

Desired
1st
3rd
th
5
th
7
10th

0.4

y [m]

0.3

0.2

VI. C ONCLUSION
In this paper, the new iterative learning control method
for the musculoskeletal arm system was proposed. Firstly,
kinematics of the system and the nonlinear muscle dynamics
were given. Next, the new iterative learning controller was
designed. The controller is composed of two parts. One is
the feedback input which consists of the task space variables,
and the other is the feed-forward input obtained throughthe iterative learning process which consists of the muscle
space variables. The results of numerical simulation showedthat the proposed controller is more robust against thesensory noises than any conventional iterative learning control method, even though there exists the nonlinear muscle
dynamics. Finally, the practical usefulness of the proposed
controller was demonstrated through the experimental result.
In this paper, the relation and analogy between the proposed
control strategy and several physiological hypotheses were
not discussed explicitly. We know that it is important toreveal such relation and analogy in order to emphasize thephysiological plausibility of the proposed method. Sincemany physiological works dealing with the relation between
the sensory feedback and feed-forward manner have beenstudied [11–13], we would like to develop the relation
between our proposed methodology and such physiologicalstudies in the future works. Also we would like to givethe stability and convergence of the proposed controller
theoretically.

0.1

0

R EFERENCES

−0.1
x [m]

0

0.1

−0.3

−0.2

Fig. 9.

Loci of the end-point position in the experiment

The loci of the end-point trajectory are shown in Fig.
9. We see from the figure that the end-point trajectory at
the first trial is slightly different from the desired one, eventhough each gain is well-tuned. This is because there still
remain certain modeling errors even though the initial control
input is obtained by the deliberate simulation beforehand.
The trajectory tracking error is gradually reduced according
to the increase of the number of trials. In the 10th trial, thetrajectory of the end-point converges to the vicinity of thedesired one. The remained small tracking error comes fromthe noise included in the visual information. Additionally,
the resultant trajectories includes a little oscillation. This
comes from that the experimental visual servoing system
has a considerable time-delay which comes from the low
sampling rate (33 [ms]) of the visual sensor. It is not serious
unless high frequency-domain movements are necessary forthe robot, and the error is acceptably small enough in thisstudy. In other words, the experimental results demonstrated
that the proposed iterative learning control method is practically useful even though there exist the nonlinear muscle[1] A. Polit A and E. Bizzi, “Characteristics of the motor programs
underlying arm movements in monkeys,” J. Neurophysiol., vol. 42,
pp. 183–194, 1979.
[2] N. Hogan, “An organizing principle for a class of voluntary movements,” J. Neurosci., vol. 4, no. 11, pp. 2745–2754, 1984.
[3] S. Arimoto, S. Kawamura and F. Miyazaki, “Bettering operation ofrobots by learning,” J. Robot. Syst.,vol. 1, no. 2, pp. 123–140, 1984.
[4] Y. Wang, F. Gao and F.J. Doyle III, “Survey on iterative learning
control, repetitive control, and run-to-run control,” J. Process Control,
vol. 19, no. 10, pp. 1589–1600, 2009.
[5] K. Tahara, S. Arimoto, M. Sekimoto and Z.W. Luo, “On controlof reaching movements for musculo-skeletal redundant arm model,”Applied Bionics and Biomechanics, vol. 6, no. 1, pp. 57–72, 2009.
[6] K. Tahara and H. Kino, “Reaching movements of a redundant musculoskeletal arm: Acquisition of an adequate internal force by iterative
learning and its evaluation through a dynamic damping ellipsoid,” Adv.
Robot., vol. 24, no. 5–6, pp. 783–818, 2010.
[7] M. L. Audu and D. T. Davy, “The inuence of muscle model complexity
in musculoskeletal motion modeling,” J. Biomech. Eng., pp. 147–157,
1985.
[8] S. Kawamura, F. Miyazaki and S. Arimoto, “Realization of robot
motion based on a learning method,” IEEE Trans. Sys., Man, Cybern.,
vol. 18, no. 1, pp. 126–134, 1988.
[9] S. Arimoto, “Robustness of learning control for robot manipulators,”
IEEE Int. Conf. Robot. Automat., pp. 1528–1833, 1990.
[10] T. Flash and N. Hogan, “The coordination of arm movements: An
experimentally confirmed mathematical model,” J. Neurosci., vol. 5,
no. 7, pp. 1688–1703, 1985.
[11] R. VanRullen and C. Koch, “Visual selective behavior can be triggeredby a feed-forward process,” J. Cog. Neurosci., vol. 15, no. 2, pp. 209–
217, 2003[12] E. Kosmidis, “Feed-forward inhibition in the visual thalamus,” Neurocomp., vol. 44–46, pp. 479–487, 2002.
[13] U. Windhorst, “Muscle proprioceptive feedback and spinal networks,”
Brain Res. Bulletin, vol. 73, 155-202, 2007.

4625