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

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

| ≤ 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 = 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 = 1,2,3. The

vectors w

,i = 1, 2,3 designate the directions of the

intermediate revolute joints, and vectors v

,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

as trigonometric functions

of the platform rotation angles Ω

,Ω

, and Ω

, i.e.

(Ω

), j = x,y,z. Similarly, the intermediate vectors,

can be expressed as functions of the input angles

, i.e. v

(θ

)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

(Ω

) · w

(θ

) = 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

to the platform angular velocities

Ω

. 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

). One

essential advantage of So-BoS is the ability to model

not only the transformation between input motor an-

gles θ

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

,θ

] the manipulator’s input joint angles,

and by β = [F

] 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

= [

] ∈ C

and

= [

] ∈ S , respectively. The matched

pairs (

, ˜µ

) ∈ 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 (

, ˜µ

),i = 1,...N.

Associated with each neuron is an activation function,

(µ), which in this case is chosen to be the softmax

function given by

(µ) =

Gkµ − ˜µ

∑

G(kµ − ˜µ

where G is a Gaussian function with variance σ

. The

normalization of U

(µ) ensures that it has a maximum

at µ = ˆµ

. The choice of σ determines the range of ac-

tivation of neighboring neurons when computing the

response of the network through

approx

∑

˜µ

(µ). (3)

Similarly, the output of the sensory system is pro-

duced by

approx

(µ) =

∑

(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 = 1,...I. In the present example N = 400

and I = 501. For each training cycle, all training

vectors ˆµ

are presented to the network and the body

icons are updated according to their respective learn-

ing laws

∆˜µ

= η

(ˆµ

− ˜µ

(ˆµ

) (5)

and

∆

(µ) = η

(β −

(ˆµ

). (6)

The parameters η

and η

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

= 10 training cy-

cles. In this example only two forces (F

and F

) were

used in the sensor space.The starting learning rates are

= η

= 0.9, with variance σ

= 1. All three param-

eters were reduced linearly to 1/N

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 (

, ˜µ

) 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) =

∑

(

β)U

(µ), (7)

where

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

∑

j=1

(˜µ

− µ)ξ

(µ). (8)

The desired output, i.e. the force balance, can be spec-

iﬁed by the choice of ξ

(

β). The right-hand side of (8)

provides the velocities of the input angles,

, 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

and θ

. The

corresponding pseudo-potential is deﬁned as

ξ(µ) = A(F

(µ) − F

(µ))

, A = 10, 000 (9)

The actual weights are computed by evaluating (9)

for each neuron j, i.e.

= ξ

(˜µ

). 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

and θ

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

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.

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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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