Application of Sensory Body Schemas to the Orientation Control of
Hand-held Tactile Tonometer
Eniko T. Enikov and Phillip Vidinski
Department of Aerospace and Mechanical Engineering, University of Arizona,
1130 N. Mountain Ave, Tucson, AZ 85721, U.S.A.
Keywords:
Spherical Parallel Mechanism, Artificial Neural Network, Body Schema, Cognitive Robotics.
Abstract:
Body schemas are a biologically-inspired approach, emulating the plasticity of the animal brains, allowing
efficient representation of non-linear mapping between the body configuration space, i.e. its generalized co-
ordinates and the resulting sensory outputs. This paper describes the development of closed-loop control of
spherical parallel mechanism based on self-learning body schemas. More specifically, we demonstrate how
a complex parallel spherical manipulator in contact with a surface of irregular geometry can be driven to a
configuration of balanced contact forces, i.e. aligned with respect to the irregular surface. The approach uses
a pseudo-potential functions and a gradient-based maximum seeking algorithm to drive the manipulator to
the desired position. It is demonstrated that a neural-gas type neural network, trained through Hebbian-type
learning algorithm can learn a mapping between the manipulator’s rotary degrees of freedom and the output
contact forces. Numerical and experimental results are presented illustrating the performance of the control
scheme. A motivating application of the proposed manipulator and its control algorithm is a hand-held eye
tonometer based on tactile force measurements. The resulting controller has been shown to achieve 10 mN of
force errors which are adequate for tactile tonometers.
1 INTRODUCTION
During the last ten years, we have seen an emer-
gence of small low-cost devices, designed to perform
some type of medical diagnostic function. Exam-
ples include a hand-held impedance plethysmograph
for measuring heart rates variation (Kristiansen et al.,
2005), various tonometers for eye pressure measure-
ments at home (Doherty et al., 2012; Polyv
´
as et al.,
2013), and vagus nerve stimulators for management
of headaches and other neurological conditions (Gaul
et al., 2014). One novel application of hand-held de-
vices is non-invasive measurement of eye pressure.
Currently, the most trusted technique for measuring
eye pressure is the Goldman applanation tonome-
tery (GAT) (Davson, 1984). GAT has to be per-
formed in a eye clinic due to the required anesthe-
sia and sterilization. Efforts to develop more conve-
nient devices for home use include tonometers such
as Reichert Tono-Pen, a non-contact air-puff tonome-
ter (Evans and Wishart, 1992), the rebound tonometer
(I-Care and I-CareONE),(Fernandes et al., 2005) and
t trans-palpebral (through the eyelid) Diaton tonome-
ter. Tono-Pen is the hand-held version of the Gold-
mann tonometer and is also based on the Imbert-Fick
law, thus requiring contact with the cornea. Reichert
7 uses an air jet, which applanates the eye, while re-
bound tonometers (I-Care and I-Care One) use an in-
duction coil to magnetize a probe and launch it against
the cornea. Diaton uses a similar principle, but in this
case, the plunger falls on the eyelid due to gravity in-
stead of induction coil (Doherty et al., 2011). This
is the only trans-palpebral tonometer currently on the
market, however it also requires the assistance of a
trained professional aligning the device to the sub-
ject’s eye. None of these existing devices have been
approved for home use and therefore gathering con-
tinuous data from patients is not possible.
This paper presents the development of a novel
positioning device, intended to achieve automatic
alignment of hand-held tonometer with respect to an
eyeball (soft sphere). In a prior work, we have inves-
tigated the forces arising from indentation of a human
eye by an array of contact probes arranged asymmet-
rically (see Fig. 1). Differences between the forces
measured by the central probe and peripheral forces
is used to determine the stiffness and hence the eye
pressure (Polyv
´
as et al., 2013). The effectiveness and
192
Enikov, E. and Vidinski, P.
Application of Sensory Body Schemas to the Orientation Control of Hand-held Tactile Tonometer.
DOI: 10.5220/0006481301920198
In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 192-198
ISBN: Not Available
Copyright © 2017 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
accuracy of these devices is often determined by their
placement and orientation with respect to the soft tis-
sue of the human body. For example, the required
accuracy of a hand-held tonometer placement should
be within ± 3 degrees, in order to obtain a valid read-
ing (Enikov et al., 2011). Consequently, successful
development of such devices requires some type of
mechanism for alignment of the device with respect
to the soft tissue.
Figure 1: Tactile tonometer applied to a human.
One particular challenge is adjustment of the three pe-
ripheral force sensors with respect the the eye ball.
Typically, an operator spends 2-5 minutes aligning the
device to the test subject’s eye. During this period,
the user adjusts the orientation of the sensor and his
eye gaze until the forces measured on three peripheral
probes are within ε according to
|F
i
F
j
| ε, i 6= j,ε > 0. (1)
Condition (1) ensures that the instrument is aligned
with respect of the eye, however achieving such align-
ment is difficult. In order to assist the user in aligning
the device, we propose a self-aligning tip, based on
a spherical parallel mechanism (SPM). SPM-s allow
rotations of the end-effector on a virtual sphere, cen-
tered at the tip of the device. Prior work on such de-
vices include the development of the agile eye (Gos-
selin and Hamel, 1994), which is a camera orienting
device. A large volume of subsequent studies have
shown that the this mechanism has large stiffness and
rapid dynamic response (Wu and Zou, 2016). The
proposed end effector is shown in Figure 2.
A total of nine revolute joints (three per kinematic
chain) are used to constrain the tip to rotate about
point P (spherical motion). In order to balance the
contact forces, one has to solve an inverse kinematic
Figure 2: Spherical Parallel Mechanism: Axes of all cylin-
drical joints point towards the center of rotation. Cylindrical
joints 1, 2, and 3 are driven by stepper motors resulting in
3-DOF motion of the triangular platform T.
problem relating the rotations of the tip to the ro-
tations of the revolute joints (Gosselin and Hamel,
1994). This classical approach requires accurate mod-
eling of the contact problem and solution of constraint
equations in real time. In contrast, the approach taken
here is based on self-learning robot, which uses bode
schemas to learn the non-linear relationship between
the anlges of the input revolute joints and the resulting
contact forces.
The pliability of body schemas and ability to op-
erate in unknown environments is one of the main
reasons a growing number of roboticists apply body
schemas, i.e. motor, tactile, visual in the devel-
opment of adaptable robots, capable of acquiring
knowledge of themselves and their environment. Re-
cent experiments in cognitive developmental robotics
have demonstrated that using tactile and vision sen-
sors, a robot could learn its body schema (image)
through babbling in front of a camera and acquiring
an ”image” of its invisible face through Hebbian self-
learning (Fuke et al., 2007).
In this paper we extend the computational ap-
proach introduced by Morasso (Morasso and San-
guineti, 1995) to create a link between the input an-
gles of the revolute joints and the tactile sensor space.
The trained network is then capable of representing a
self-learned body schema allowing control of the end
effector in a feed-forward mode. A unique feature of
the approach is that the robot control task does not
require the use of inverse kinematics. These features
of the proposed control scheme are illustrated in the
subsequent sections of this paper.
Application of Sensory Body Schemas to the Orientation Control of Hand-held Tactile Tonometer
193
2 SELF-ORGANIZING BODY
SCHEMA OF MAV-s
2.1 Classical 3-DOF Manipulator
Model
The SPM is modelled using the coordinates of the unit
vectors representing the axis of each joint (see Fig.
3). The vectors u
i
,i = 1,2,3 are fixed in space and are
represent the axis of rotation of the driving motors.
Each of
Figure 3: Unit-vectors of Revolute Joints.
these joints rotates through angles θ
i
,i = 1,2,3. The
vectors w
i
,i = 1, 2,3 designate the directions of the
intermediate revolute joints, and vectors v
i
,i = 1,2,3
represent the directions of the distal joints attached to
the end effector. Using standard matrix algebra, one
can express the vectors v
i
as trigonometric functions
of the platform rotation angles
x
,
y
, and
z
, i.e.
w
i
(
j
), j = x,y,z. Similarly, the intermediate vectors,
w
i
can be expressed as functions of the input angles
θ
i
, i.e. v
i
(θ
i
)i = 1, 2,3 (Gosselin and Lavoie, 1993).
To obtain an input-output kinematic relationship, one
uses the obvious constraint between the normal vec-
tors
v
i
(
j
) · w
i
(θ
i
) = cos(α), i = 1,2, 3, j = x, y,z (2)
where α is the angle between the two vectors (see Fig.
4).
Equations (2) represent a non-linear transforma-
tion between input and output angles. Under a classi-
cal approach, its time derivatives result in the inverse
Jacobian needed to relate the input anglular veloci-
ties
˙
θ
i
to the platform angular velocities
˙
j
. With
the position of the end plate determined, one can use
linear force-displacement relationships to determine
the contact forces. An equivalent model was imple-
mented in Matlab Simmechanics as a way of testing
the neural network-based approach presented next.
Figure 4: Angles Between Directional Unit-Vectors.
2.2 Body and Sensor Schemas
The use of body and sensor schemas is an alternative
to the classical method described in the previous sec-
tion. Rather than using an analytical model such as
(2), a self-organizing body schema (So-BoS) can be
used to link the manipulator’s output (sensory) space
S with its input (configurational) space C . A detailed
review of applications of body schema-s in robotics
can be found in (Hoffmann et al., 2010). As an exten-
sion of the approach of Morasso (Morasso and San-
guineti, 1995) and Stoychev (Stoytchev, 2003), in-
stead of vision data, the sensor space of the proposed
SPM manipulator contains contact forces measured
by the three peripheral probes F = (F
1
,F
2
,F
3
). One
essential advantage of So-BoS is the ability to model
not only the transformation between input motor an-
gles θ
i
and the position of the end-effector, but also to
predict the resulting forces. These forces are a func-
tion of the position of the hand-held unit with respect
to the eye, i.e. an unknown error is introduced by the
user.
Similar to conventional self-organizing neural net-
work maps, a layer of neurons (processing units) is
used to learn the mapping between the configuration
space (generalized position of the robot) and the out-
put of the tactile force sensors. Unlike other topo-
logically ordered self-organizing maps such as the
Kohonnen map (Kohonen, 1982), the neurons in the
present approach are initially disordered, i.e. form-
ing a ‘’neural gas” (Martinetz et al., 1991). The
training process modifies the weights of each neu-
ron until the network learns N body icons represent-
ing the C S -space. More specifically, denoting by
µ = [θ
1
,θ
2
,θ
3
] the manipulator’s input joint angles,
and by β = [F
1
,F
2
,F
3
] the vector of contact sensor out-
puts, then for each body position i, the generalized co-
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
194
ordinates and associated sensors outputs will present
an instance of these two vectors ˜µ
i
= [
˜
θ
i
1
,
˜
θ
i
2
,
˜
θ
i
3
] C
and
˜
β
i
= [
˜
F
i
1
,
˜
F
i
2
,
˜
F
i
3
] S , respectively. The matched
pairs (
˜
β
i
, ˜µ
i
) C S are referred to as body icons. The
C S space is approximately by a field of N neurons,
each storing a learned body icon (
˜
β
i
, ˜µ
i
),i = 1,...N.
Associated with each neuron is an activation function,
U
i
(µ), which in this case is chosen to be the softmax
function given by
U
i
(µ) =
Gkµ ˜µ
i
k
j
G(kµ ˜µ
i
k)
,
where G is a Gaussian function with variance σ
2
. The
normalization of U
i
(µ) ensures that it has a maximum
at µ = ˆµ
i
. The choice of σ determines the range of ac-
tivation of neighboring neurons when computing the
response of the network through
µ
approx
=
N
j
˜µ
j
U
j
(µ). (3)
Similarly, the output of the sensory system is pro-
duced by
β
approx
(µ) =
N
j
˜
β
j
U
j
(µ). (4)
The network training process is based on a compet-
itive learning process, where the N neurons are pre-
sented with a large number of pseudo-random training
vectors ˆµ
l
,l = 1,...I. In the present example N = 400
and I = 501. For each training cycle, all training
vectors ˆµ
l
are presented to the network and the body
icons are updated according to their respective learn-
ing laws
˜µ
j
= η
1
(ˆµ
l
˜µ
j
)U
j
(ˆµ
l
) (5)
and
˜
β
j
(µ) = η
2
(β
˜
β
j
)U
j
(ˆµ
l
). (6)
The parameters η
1
and η
2
are the learning rates for
each law, respectively. The competitive learning pro-
cess involves reduction of the learning rate as well as
the range of activation specified by σ as the training
proceeds. Through (4), the trained network represents
a mapping between the manipulator’s configuration
space, C and the resulting sensor space, S . Therefore,
it is an implicit calibration procedure.
Figure 10 presents the 501 training vectors (blue
dots) and the learned body icons (green circles) upon
training of N = 400 through N
T
= 10 training cy-
cles. In this example only two forces (F
1
and F
2
) were
used in the sensor space.The starting learning rates are
η
1
= η
2
= 0.9, with variance σ
2
= 1. All three param-
eters were reduced linearly to 1/N
T
of their starting
values at the end of the last training epoch.
Figure 5: Training Force Data and Output of Trained Net-
work.
One of the greatest benefits from the trained neural
network and the associated mapping (4) is its ability
to generate robot trajectories in the sensor space with-
out explicitly computing its inverse Jacobian. This
property of the body-schema based approach is illus-
trated in the next section.
3 TRAJECTORY PLANNING IN
THE FORCE SPACE
Upon training, each processing unit has its preferred
body icon (
˜
β
i
, ˜µ
i
) allowing representation of the ma-
nipulator’s sensory output through (4). In addition to
the sensory output, the trained network can define ad-
ditional functions over the configuration space or the
sensory space. The present application requires path
planning leading to a configuration where the forces
are balanced according to (1). The advantage of the
method is that the trained network does not require
explicit inversion of the mapping between the manip-
ulator’s position and the output of the force sensors.
Instead, the trajectory can be obtained through solu-
tion of a ordinary differential equation representing
a gradient descent on a user-defined pseudo-potential
field. More specifically, we use a pseudo-potential de-
fined over the force space through
ξ(µ) =
j
˜
ξ
j
(
ˆ
β)U
j
(µ), (7)
where
˜
ξ
j
are scalar weights for each processing unit.
The potential weights can be selected such, that the
resulting pseudo-potential has an extrema (for exam-
ple maximum) at the target landing location. Then
a simple ordinary differential equation can be formu-
lated that has a maximum- or minimum-seeking solu-
tion. Following the method of (Stoytchev, 2003), we
Application of Sensory Body Schemas to the Orientation Control of Hand-held Tactile Tonometer
195
use a gradient ascend equation to drive the manipula-
tor’s input angular coordinates to the maximum of the
pseudo-potential
˙µ = γ∇ξ(µ) = γ
N
j=1
(˜µ
j
µ)ξ
j
U
j
(µ). (8)
The desired output, i.e. the force balance, can be spec-
ified by the choice of ξ
j
(
ˆ
β). The right-hand side of (8)
provides the velocities of the input angles,
˙
θ
i
, while its
solution generates the trajectory.
To illustrate the approach, we have a two-
dimensional example where the pseudo-potential be-
comes a surface over the coordinates θ
1
and θ
2
. The
corresponding pseudo-potential is defined as
ξ(µ) = A(F
1
(µ) F
2
(µ))
4
, A = 10, 000 (9)
The actual weights are computed by evaluating (9)
for each neuron j, i.e.
˜
ξ
j
= ξ
a
(˜µ
j
). The correspond-
ing pseudo-potential surface is shown in Figure 6 for
N=200 neurons.
(a)
Figure 6: Pseudopotential surface ξ over the input angles θ
1
and θ
2
.
Solving equation (8) for a given pseudo-potential re-
sults in trajectories leading towards the target posi-
tion. Figure 7 shows the convergence of the method
for three initial conditions (IC-s) using the solution of
(8) with N=800 neurons.The method was also tested
experimentally as described in the next section.
4 EXPERIMENTAL VALIDATION
The validation of the proposed algorithm was carried
out using a custom-designed experimental apparatus.
A 3-DOF manipulator driven by three stepper motors
Figure 7: Simulated Trajectories For σ = 1 and σ = 0.1.
Larger σ results in smoother maps and smaller steady-state
errors.
Figure 8: Experimental Apparatus.
was constructed as shown in Figure 8. A soft neo-
prene sphere was placed over the force sensors to em-
ulate the presence of an ”eye”.
The experiment was carried out in two phases -
training phase, where the SPM input angles θ
i
were
driven randomly in a range avoiding the kinematic
singularities. The network was trained with the result-
ing force data and subsequently used in a closed-loop
control configuration as illustrated in Figure 9.
The resulting controller is a form of feed-forward
controller since the output forces are not fed back into
the controller. Only position coordinates of the con-
figuration space are needed, which are typically mea-
sured by the encoders of the motors.
Figure 10 shows the training data collected during
3.5 seconds of motion. One can notice that the force
data is very irregular and noisy as is the case of man-
ual positioning of the tonometer against the eye.
Upon turning on the controller, the two forces
reach equal values within 3.5 - 4 seconds as illustrated
in Figure 11.
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
196
Figure 9: Training and Closed-Loop Control Phases of
SPM.
Figure 10: Experimental Results: Training Data.
Figure 11: Experimental Results: Force Convergence.
In order to assess the sensitivity of the method with
respect to the number of training cycles, i.e. ability
to shorten the training period, the experiment was re-
peated with 5 and 7 training cycles, respectively. The
force convergence for each case is shown in Figure
12. Clearly the performance degrades as the number
of training cycles is decreased.
Figure 12: Experimental Results: Force Convergence using
5 (top) and 7 (bottom) training cycles.
5 SUMMARY AND
CONCLUSIONS
The application of self-organizing artificial neural
networks to the problem of controlling a manipulator
in contact with a soft tissue has been described. It has
been demonstrated that the neural network can fuse
seamlessly the information gathered from multiple
imperfect force sensors and significant noise. Upon
Application of Sensory Body Schemas to the Orientation Control of Hand-held Tactile Tonometer
197
training period of 3.5 seconds, the network was able
to drive the SPM manipulator to the desired balanced-
force condition. The accuracy of the positioning is
a function of the standard deviation (interaction dis-
tance) of neighboring neurons as well as the rate of
descent. A total of 200 neurons trained over 10 cycles
were used in the experiments, which resulted in fast
training. A minimum of ten training cycles were re-
quired in order to produce robust controller, capable
of balancing the forces within 10 mN. This force error
corresponds to approximately 1 mmHg of error in tac-
tile tonometery (Enikov et al., 2015). Therefore, the
proposed approach appears suitable for implementa-
tion in a hand-held devices for diagnostic purposes.
ACKNOWLEDGMENTS
The authors acknowledge the partial support of NSF
grant # 1446098.
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