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Oculomotor Control


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The main aim of oculomotor control is to drive the eyes in a rapid, stable, and coordinated fashion to provide accurate bifixation of targets in space. Eye movement measurements have provided quantitative assessments of these control processes. Indeed, advances in eye movement measurement technology and cortical imaging techniques will continue to provide deeper insights into neurological processes that guide oculomotor responses under both normal and disease conditions.
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Eye movements are accurate reflections of the brain’s
control strategy. Their function is to provide essential
information about the visual scene under a wide variety
of conditions encountered in daily life. Therefore, the
understanding of the control of eye movements, or oculo-
motor control, is one of the most important goals of vision
scientists and bioengineers.
When one redirects gaze, neural command signals from
the brain centers change the lens focus and rotate the two
eyes to provide a clear and single image of the new target.
It has been found that three primary oculomotor move-
ments are involved in the automatic control of binocular
gaze. Accommodation, or focusing, changes the lens power
to provide clear vision; vergence rotates the eyes symme-
trically in opposite directions to provide singleness of
vision; and version (saccades and pursuit) rotates the
eyes in the same direction to track lateral displacements
of the target. These oculomotor systems use automatic
feedback to provide accurate responses to target change.
Viewed in engineering terms, they can be represented as
feedback control systems that are drawn as block dia-
grams. Moreover, well-known engineering control systems
theories can be used to study the feedback control proper-
ties of these physiological processes.
2.1. The Eye
The goal of the accommodation, or focusing, system is to
provide a clear and sharp image of an object on the retina.
Figure 1 shows a cross-sectional view of the interior of the
human eyeball (1). Light rays enter the eye first through
the transparent cornea, which comprises about two thirds
of the fixed refractive power of the eye. The rays then pass
through the opening in the iris, called the pupil, and are
refracted by the transparent lens, which comprises the
remaining one third of the fixed optical power. The lens
has, in addition, a variable component that is controlled by
the ciliary muscle (which is part of the ciliary body)
through its action via the zonular fibers between the
ciliary body and the lens. In this way, the light rays of a
target at different distances can be focused by the vari-
able-powered lens onto the fovea, which is a small high-
acuity region on the retina.
2.2. Extraocular Muscles
The goal of the vergence and versional eye movement
systems is to provide a single percept by bringing the
images of a target onto corresponding retinal points in the
two eyes. Hence, when the target moves in depth, the
eyeball in each eye must be rotated by the muscles on the
outside of the eyeball, called extraocular muscles (Fig. 2),
to once again bring the images in register on the retinas
(2). Three pairs of extraocular muscles are concerned with
horizontal, vertical, and oblique rotations of the eye.
Vergence and version use primarily the horizontal mus-
cles, called the medial rectus and lateral rectus, that are
reciprocally innervated and rotate the eye in the horizon-
tal plane. Neural signals from higher brain centers drive
the two eyes in a coordinated fashion so that the visual
lines intersect at the target. The resulting images in the
two retinas are combined by the brain to form a single
3.1. Accommodation
The act of focusing, or accommodation, from a far (F) to a
near (N) target is shown schematically in Fig. 3 (3).
Initially, light rays from the far target (F; solid lines) are
focused on the fovea (f). The sudden introduction of a near
target (N; dashed lines) moves the focal point beyond the
retina, which results in a blur circle on the retina. The
accommodative, or focusing, response changes the curva-
ture of the front of the lens and moves the underconverged
light rays forward (see arrow) to bring the rays back into
focus at the fovea.
3.2. Vergence and Version
When a target is displaced in depth (Fig. 4a) (4), an
angular difference between the near and far targets, called
disparity, is created (this is represented by the angular
displacements indicated by the curved arrows). The angu-
lar difference causes the two eyes to rotate in opposite
Optical axis Cornea
Figure 1. Horizontal section of the eye showing the major ocular
components for accommodation.
Wiley Encyclopedia of Biomedical Engineering, Copyright &2006 John Wiley & Sons, Inc.
directions to track it in a disjunctive manner, called
vergence. Convergence is the response to a far-to-near
target displacement, whereas divergence is the response
to a near-to-far displacement. In contrast, when a target is
moved laterally from side to side (Fig. 4b), the two eyes
rotate in the same direction to track it in a conjugate, or
versional, manner. There are two types of versional eye
movements: saccades that jump to follow rapid target
displacements, and pursuit eye movements that smoothly
follow relatively slowly moving targets.
A basic general feedback control system block diagram is
shown in Fig. 5. The error E(s), or the difference between
the input X(s) and the product of the output and feedback
gain YðsÞHðsÞ, serves as the driving signal for the for-
ward-loop gain G(s). It can be shown that the overall
transfer function is given by
FðsÞ¼ YðsÞ
It turns out that this apparently simple equation is the
basis for much of control systems theory. It can be seen
that if G(s)H(s) equals 1, the system would become
unstable. This result can occur, for example, if within
the term G(s)H(s), the gain is too high or the latency is too
long. Indeed, much of control systems theory involves the
determination of the conditions for instability and the
system modifications needed to avoid arriving at these
unstable conditions.
Experimental results in both the accommodation and
vergence eye movement systems have shown that their
latencies (370 and 200 ms, respectively) and dynamic
response times (250 and 200 ms time constants, respec-
tively) are at about the same time ranges. Thus, the
Figure 3. Schematic diagram of the accom-
modative response.
ff ff
Figure 4. Schematic drawing of (a) pure symmetric vergence and
(b) pure versional eye movements. LE, left eye; RE, right eye; f,
Visual line Visual line
Medial rectus
Axis of muscle Axis of muscle
Superior rectus
Lateral rectus
Figure 2. The two eyes and the extraocular
muscles as seen from above.
response after a latency could be in the opposite direction
as the ongoing stimulus. Hence, if a simple feedback loop
were used in a model of the system, the responses could
consist of instability oscillations. It turns out that both of
these systems solve this problem by separating their
control process into two parts: a fast open-loop component
and a slow closed-loop component. The fast component
responds to the stimulus amplitude without feedback to
arrive near the desired position. The absence of any feed-
back (even though sensory input continues to be available)
ensures stability of the initial response. Then, when the
response amplitude is close to the stimulus amplitude, a
slow closed-loop component takes over and reduces the
small residual error to a minimum. Because the residual
error is small during the slow-component stage of the
response, the gain of the slow component can be relatively
low and still achieve adequate dynamic response. Yet, once
these two processes are completed, the overall error would
be small, and the effective steady-state gain would be
equivalent to a continuous feedback system with a high
forward-loop gain (with its inherent instability problems).
Thus, this dual-mode process achieves both rapid dy-
namics and small residual error without sacrificing stabi-
The saccadic system also has a long latency (200 ms)
compared with its relatively fast response dynamics
(duration of about 50 ms for a 10 deg saccade), and thus
would similarly have instability problems if it were mod-
eled as a simple continuous feedback system. It solves this
problem by responding with an initial open-loop move-
ment, but unlike the accommodation and vergence sys-
tems, it uses subsequent saccades to make corrective
movements. The pursuit system has a similar latency as
saccades. It preclude instabilities by estimating and then
tracking the target velocity, and defers to saccadic track-
ing at target velocities higher than about 30 deg/s.
6.1. Accommodation Model
6.1.1. Static. The accommodation system senses blur of
the retinal image and varies the lens power with neuro-
logical feedback control to reduce blur to a minimum (5–7).
A descriptive block diagram of the accommodation system
is shown in Fig. 6a (8,9). The difference between target
distance and focus distance provides the retinal-image
defocus whose sensory output, or blur, is processed by the
accommodative controller following a time delay. The
controller output is summed with the tonic signal (which
represents the response under the no-stimulus condition)
to drive the accommodative plant, or lens. The feedback
loop reduces the blur to a minimum to provide clear focus
of the target image on the retina.
A more detailed version of the model is shown in Fig.
6b. The deadspace element (with ‘‘breakpoints’’ at 7DSP)
represents the depth of focus. The accommodative con-
troller gain (ACG) represents the central neurological
control of accommodation. The tonic term (ABIAS) repre-
sents the state of accommodation when the system is
rendered open loop, and it has been called ‘‘dark focus’’
and ‘‘night myopia’’ (11–13), but is more appropriately
called ‘‘tonic accommodation’’ (TA) because it is obtained
under a wide range of conditions including darkness,
empty field, and pinhole-viewing (14–16). The saturation
element (Sat) limits the amplitude of the lens response. It
is used to represent the decline in lens response range
with age, corresponding to the clinical condition of pres-
byopia (17).
6.1.2. Dynamic. As discussed above, the difficulties
that had been encountered in earlier continuous models
of accommodation in obtaining a stable response were due
to the inherent problem of having relatively slow dy-
namics (time constant ¼250 ms) and a long time delay
(350–400 ms) in the accommodative feedback loop. Thus,
the observed instantaneous accommodative output is ac-
tually a response to a controller signal (AE ¼AS AR)
that had occurred 370 ms earlier. If AE had changed sign
(e.g., from positive AE, or lag of accommodation, to
negative AE, or lead of accommodation) during the inter-
vening delay interval, the accommodative output would be
in the opposite direction. For dynamically changing ac-
commodative stimuli, this could lead to repeatedly inap-
propriate responses, and in turn instability oscillations.
To overcome these difficulties, a dual-mode model of
accommodation was developed (8,18). The overall block
diagram of the model is shown in Fig. 7a. The first block is
a dead-space operator, which represents depth of focus,
with limits equal to 70.12 diopters (D, equal to the
Distance Focus
Blur Delay Controller Plant
Delay ACG Sat
Figure 6. Hung’s (8,9) accommodation system models: (a) De-
scriptive model, (b) A more detailed model.
X(s) E(s)
Figure 5. Block diagram of a general feedback control system.
reciprocal of the distance from the eye to the target in
meters). The controller has both fast and slow compo-
nents. The fast component is derived from the sum of the
visual feedback error signal and the neurological efference
copy signal (not shown in Fig. 7a), which is derived from
the fast component output. This results in an open-loop
stimulus signal that is nearly equal to the original stimu-
lus amplitude. This open-loop drive is important for two
reasons. First, it maintains stability in the presence of a
relatively long latency (370 ms); and second, it meets the
requirement of an accurate initial step response. The
open-loop fast component movement accounts for most of
the step response amplitude, with the remainder being
taken up by the slow closed-loop component. The resulting
accurate response corresponds to a very high gain in a
continuous feedback control system, which would have
otherwise resulted in instability oscillations.
The accommodation model was used to simulate (see
Fig. 7b) responses to pulse (top trace, 0.32 s stimulus
duration) and square-wave (frequency, in hertz, as shown
at right of traces) stimulation having an amplitude of 2D
(18). The simulated responses are in good agreement with
experimental results. Similar accurate simulation re-
sponses have also been obtained for ramp and sinusoidal
stimuli (18; not shown).
6.2. Vergence Model
6.2.1. Static. Hung and Semmlow (13) developed a
static vergence system model (not shown). Its configura-
tion is the same as the accommodation system model
above (Fig. 6b), except the names of the elements are
replaced by: vergence stimulus (VS); vergence response
(VR); dead-space range 7DSP, which represents the dis-
parity threshold range called Panum’ fusional area (19);
vergence controller gain (VCG); and VBIAS, which repre-
sents tonic vergence.
6.2.2. Dynamic. Hung et al. (20) developed a dual-
mode model of the vergence system (not shown). It con-
sisted of a fast open-loop component and a slow closed-loop
component (similar to the dynamic accommodation model
shown in Fig. 7a). Simulation responses to positive (con-
vergent) ramp stimuli (amplitude of 4 deg) are shown in
Fig. 8, with velocity in deg/s shown at right of traces.
Dotted line ¼stimulus, and solid line ¼response. The
simulation responses showed good fit to experimental
0 2 4 6 8 10
Pulse & Square Wave Responses
Accommodation (D)
Time (sec)
Figure 7. (a) Overall block diagram of dual-
mode accommodation model. (b) Dual-mode
accommodation model responses to pulse and
square-wave stimulation.
data. Note that for ramp stimuli between 3 and 10 deg/s,
there are multiple-step movements, which are also seen in
the experimental responses (20). Accurate simulation
responses were also obtained for sinusoidal stimuli (20;
not shown).
6.3. Version Models
6.3.1. Saccade. Young and Stark (21) developed a sac-
cadic system model (Fig. 9a). The retinal error is input to a
sampler with an experimentally determined 200-ms sam-
pling interval. The dead zone represents the threshold
range before a response develops. The computing delay
represents the latency of the saccadic response, and it is
given by exp( sT), where T¼200 ms. The integrator 1/s
integrates the retinal error signal, and its output is
summed with any mechanical or neural disturbance in-
put. Muscle dynamics is represented by a second-order
low-pass filter. Finally, the eye angle output is fed back to
be subtracted from the target angle to provide the retinal
Figure 8. Vergence model responses to ramp stimuli.
1 2 3
Eye (deg) Target (deg)
Light off Light on
Figure 9. (a) A sampled-data model of the
saccadic system. (b) Pursuit system model. (c)
Saccade and pursuit eye movement responses.
Note that ordinate scales are reversed for
target and eye responses.
6.3.2. Pursuit. Lisberger et al. (22) developed a pursuit
system model (Fig. 9b). Image motion provides the central
command to the efferent pathways. The negative feedback
pathway (lower dashed line) represents the change in the
eye direction due to the physical eye motion, and the
positive feedback pathway (upper solid line) provides a
hypothesized pursuit neural command for eye velocity.
The mathematical addition of the positive feedback of eye
velocity command signal and the visually derived retinal
error velocity (target velocity minus eye velocity) provides
a reconstructed target velocity signal. The main effect of
the reconstructed signal is to provide stability in the
pursuit eye movement dynamics.
6.3.3. Saccadic and Pursuit. The time courses of saccade
and pursuit eye movement responses (bottom trace) and
the sinusoidal lateral target motion (top trace) are shown
in Fig. 9c (6). Initially, smooth target motion permits the
pursuit system to track the target. However, when the
target is extinguished (i.e., lights off), only the memory of
repetitive target swing guides the eyes, and the saccadic
system takes over and uses a series of fixations to approx-
imate the trajectory of the unseen target. When the target
reappears, smooth tracking promptly returns.
7.1. Accommodation and Vergence Interactions
It has been found experimentally that accommodative
error (i.e., blur) alone can drive accommodation as well
as vergence. The latter is called accommodative-conver-
gence (23). Moreover, vergence error (disparity) alone can
drive vergence as well as accommodation. The latter is
called convergence-accommodation (24). Thus, there is
direct influence from one system to the other. Moreover,
when both accommodative and vergence stimuli are pre-
sent, which is normally the case, these two systems form
an interactive dual-feedback system.
A nonlinear static model of interactive dual-feedback
accommodation and vergence system (9,13) is shown in
Fig. 10. It contains the dead-space operators depth of focus
and Panum’s fusional area. The dead space between þ
and AD simulates the depth of focus (AD¼0.15 D). The
output of the dead-space operator is multiplied with ACG
to give the accommodative controller output. Similarly,
the dead space between þand VD simulates Panum’s
fusional area (VD ¼6 min. of arc). The output of the
dead-space operator is multiplied with the VCG to give
the vergence controller output. The terms AC and CA
represent accommodative-convergence and convergence
Figure 10. Nonlinear static model of inter-
active dual-feedback accommodation and ver-
gence system.
Figure 11. Neural pathways for saccade and vergence.
accommodation cross-link gains, respectively. Also, ABIAS
and VBIAS represent tonic accommodation and tonic
vergence, respectively. The model responses have been
shown to accurately simulate experimental responses for
a variety of congruent as well as noncongruent (i.e.,
unequal accommodative and vergence) stimuli (9).
7.2. Saccade and Vergence Interactions
There has been a great deal of controversy regarding
saccadic and vergence responses to nonsymmetrical sti-
muli (i.e., targets that are not positioned along the midline
formed by an imaginary line from the midpoint between
the two eyes and the straight-ahead target position)
(25,26). It began with the experimental observation that
the responses do not seem to be a superposition of the
individual saccadic and vergence components (27). Some
researchers have claimed that the act of executing a
vergence response influenced the saccadic response, and
that the manner of this influence may be different depend-
ing on the environmental ‘‘natural’’ scenery seen by the
eyes (27–30). This claim, however, created much uncer-
tainty about the exact properties of the saccadic and
vergence systems that would result in these changes. To
resolve this uncertainty, a differential latency theory,
which was not dependent on the nature of the scenery,
has been proposed (25,26). The theory clearly explains the
underlying mechanism for the observed non-superposed
The differential latency theory (25,26) states that the
transient divergence observed during saccade–vergence
responses can be accounted for by a small difference in the
latencies between the contralateral (opposite sides) and
ipsilateral (same side) neural pathways driving the con-
jugate eye movement (Fig. 11).
For saccades, horizontal burst neurons (B) and tonic
eye position neurons (T) in the midbrain paramedian
pontine reticular formation (PPRF) provide similar input
signals to both lateral rectus motoneurons (LR) and inter-
nuclear neurons (I) in the abducens nucleus (VI). The
abducens internuclear neurons cross the midline and
ascend in the medial longitudinal fasciculus (MLF) to
drive the medial rectus motoneuron. On the other hand,
for vergence, the presumed complementary vergence sig-
nals, c and c-, innervate the ipsilateral MR and LR to drive
the response.
Because of the brief latency difference (B6 ms) between
these two neuronal pathways (31), there is a transient
difference in the movement in the two eyes, which is
exhibited as transient divergence during conjugate eye
movement in the ipsilateral direction. Indeed, the differ-
ential latency model (Fig. 12) has been shown to accu-
rately simulate the experimental responses for a variety of
congruent and noncongruent stimuli (25,26).
For example, representative experimental time traces
under the free-space (FS; i.e., natural-viewing) environ-
ment are shown in Fig. 13a (left column) for stimulus
requiring a response of 4 deg in the LE and 8 deg in
the RE (positive and negative numbers represent right-
0.006s +1
Delay Disjunctive
trans. func.
Delay Conjugate
trans. func
Left LR
Left MR
Left eye
Right ey
Right MR
Right LR
Figure 12. Dynamic saccade-vergence model.
ward and leftward target displacements, respectively),
which correspond to 4 deg of convergence and 6 deg of
leftward versional movement (25,26). Representative ex-
perimental time traces under the instrument-space (IS;
i.e., optical bench) environment are shown in Fig. 13b
(right column) for stimulus requiring a response of 2 deg
in the LE and 6 deg in the RE, which correspond to 4 deg
of convergence and 4 deg of leftward versional movement.
For both columns, the top graph shows left eye (LE, upper)
and right eye (RE, lower) time traces. The second graph
shows conjugate (dotted) and disjunctive (solid) amplitude
time courses. The third graph shows the disjunctive
velocity time course. The bottom graph shows top-view
binocular fixation trajectories corresponding to the move-
ments shown in the top graph. The initial central fixation
point and the target are shown as ‘‘ þ’’ symbols. The
circular-shaped iso-vergence arcs (dotted) are separated
at 5 deg intervals, whereas the radial lines (dashed) are
separated at 10 deg intervals. Note that for the bottom
graph under the FS environment (a), the trajectory, start-
ing from a position indicated by the central fixation cross,
consists of an overshoot loop followed by a radially direc-
10 10
RE & LE amplitude (deg)
Conj & Disj amp (deg)
Disj Vel (deg/sec)
Distance (cm)
0.2 0.4 0.6 0.8 1
00.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1
00.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1
00.2 0.4 0.6 0.8 1
010 010
Time (sec)
Left-right (cm) Left-right (cm)
Time (sec)
Figure 13. Experimental responses under (a)
free-space and (b) instrument-space environ-
ted vergence movement towards the target. On the other
hand, under the IS environment (b), the trajectory con-
sists of an initial convergence (along the central radial
line), followed by a saccadic trajectory, which is then
followed by a final convergence movement (along another
radial line).
Model simulation responses are shown in Fig. 14 for a
target displacement requiring 2 deg in the left eye and
6 deg in the left eye, which corresponds to 4 deg of
convergence and 4 deg of leftward saccadic response for
the conditions of (a) simultaneous (latency ¼200 ms) and
(b) sequential (latency: disjunctive ¼200 ms; and conju-
gate ¼300 ms) onset of controller signals (25,26). The
description of the traces are the same as those for Fig. 13.
The model simulations show how the latency difference
in the two neural pathways can account for the experi-
mental findings. Indeed, these results are in agreement
with Hering’s law, which states that the two eyes act as
one, so that the separate conjugate and disjunctive con-
10 10
RE & LE amplitude (deg)
Conj & disj amp (deg)
Disj vel (deg/sec)
Distance (cm)
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1
010 010
Time (sec)Time (sec)
Left-right (cm) Left-right (cm)
Figure 14. Model responses for (a) simulta-
neous and (b) sequential onset of controller
trollers work together to drive the eyes toward the target
in space.
Static linear and nonlinear model elements serve impor-
tant roles in shaping the steady-state accommodative and
vergence responses and provide insights into clinical
abnormalities. Also, the dynamic characteristics of these
models have revealed how these systems attain both
stability and rapid motor responsivity. For both the ac-
commodation and vergence systems, whose latencies are
long relative to their dynamics, a continuous feedback
control process would lead to instability oscillations. It
turns out that the strategy used is to respond with an
initial fast open-loop movement that provides a large
portion of the response amplitude, followed by a slow
closed-loop movement that reduces the residual error to
a minimum. In this way, dynamic responsivity and accu-
racy is attained without introducing instability oscilla-
A similar strategy is used by the versional eye move-
ment systems. The saccadic movement is driven by open-
loop control, which is followed by small secondary sac-
cades to reduce the residual error. Thus, rapid dynamics
are achieved while maintaining accuracy and stability. For
the pursuit system, the strategy is to estimate and then
track the target velocity, thus maintaining stability in the
Moreover, when these systems operate together, as is
generally the case in daily life, their responses are not just
simple summations of their isolated open-loop motor
responses. For example, the neural linkage between the
accommodation and vergence control processes results in
a combined interactive dual-feedback control system that
is quite complex. Also, in the saccadic and vergence
systems, the finding of dynamic interactions had lead to
some confusion regarding the underlying control pro-
The primary problem with saccade and vergence inter-
actions is that both saccade and vergence share the same
motor output, namely, the extraocular muscles that rotate
the eyeballs. Hence, their individual contributions must
be inferred from the eye movement responses. It has been
suggested in recent years by some investigators that
vergence responses are facilitated by saccades depending
on the characteristics of the visual scene. However, the
differential latency theory has clarified this by showing
that the transient vergence contribution during a saccade
is caused by a small difference between peripheral neural
delays of the signals to the two eyes, and not by differences
in the visul scene.
The main aim of oculomotor control is to drive the eyes
in a rapid, stable, and coordinated fashion to provide
accurate bifixation of targets in space. Eye movement
measurements have provided quantitative assessments
of these control processes. Indeed, advances in eye move-
ment measurement technology and cortical imaging tech-
niques will continue to provide deeper insights into
neurological processes that guide oculomotor responses
under both normal and disease conditions.
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Conference Paper
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Eye movements have the goal of optimizing visual perception, therefore the investigation of eye motion strategies play an important role in the design of humanoid robot eye systems. Saccades in humans and primates is a significant class of ocular motions, which obey the so called Listing's Law, which constrains the admissible eye's angular velocities and ensure zero torsion during motion. In this paper we present a model of the eye plant proving that listing's law implementation is strongly related with the geometry of the eye and its actuation system (extraocular muscles). The proposed model has been used to provide the guidelines for the design of a tendon driven humanoid robot eye. Experimental tests, presented in this paper, validate the model by performing a quantitative comparison of the performance of the robot eye with physiological data measured in humans and primates during saccades
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This paper presents a new tendon driven robotic eye. The system has been designed to emulate the actual saccadic and smooth pursuit movements performed by human eyes. The system consists of a sphere (the eye-ball), actuated by four independent tendons driven by four DC motors, integrated in the system. The eye-ball hosts a miniature CMOS color camera and is hold by a low friction support allowing three rotational degrees of freedom. Optical sensors provide feedback to control the correct tendons' tensions during operations. The control of the eye is performed by means of an embedded controller connected to a host computer using CAN bus
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