COMPLEXITY REDUCTION IN CONTROL OF HUMAN HAND

PROSTHESIS FOR A LIMITED SET OF GESTURES

Giovanni Saggio, Pietro Cavallo, Daniele Casali and Giovanni Costantini

Department of Electronic Engineering, University of Rome “Tor Vergata”, Rome, Italy

Keywords: Hand prosthesis, Data glove, HMI.

Abstract: This paper carried out a statistical analysis of human finger’s joint angles during hand specific daily

activities, studying the correlations among the joints and applying a linear regression to express their

correlations. The aim was to reduce the number of myoelectric sensors necessary in devices such as

prosthesis, stands the current surgery difficulties and the problem of rejection, but without losing too many

degrees of freedom. Measures were taken using our special hand movement acquisition system called

HITEG data glove. As a preliminary work, we decided to limit the set of gestures performed to 9 of the

most common movements of the human hand. The results shown that the number of sensors can be reduced

from 14 to 7 with an acceptable error on the presumed value of each finger joint angle which can be as low

as 10 degrees.

1 INTRODUCTION

Myoelectric prosthetic hands are used to replace

functions of a natural hand lost by amputation.

Motor functions of such myoelectric hands can

almost be compared to that of a natural hand

(Shadow Robot Company, 2003). They have a very

high number of joints and actuators, which bring up

to 20 Degrees of Freedom (DoF). Unfortunately this

technology cannot be fully exploited by current hand

prosthesis (Carrozza et al., 2003 - Micera et al., 2002

- Craelius et al., 1999). The main limitation regards

the sensor system that allows to control the robotic

hand: a set of myoelectric sensors is placed above

the attachment of the prosthesis to the arm: every

joint with an own DoF of the hand needs a specific

myoelectric sensor, but placing 20 different

myoelectric sensors is not only practically difficult:

it also increments the possibility of a rejection.

Hence only few myoelectric sensors can be

reasonable used, and this affects the DoF available

to perform a gesture.

The purpose of this work is to study the

correlations among joint angles while performing

most common and useful movements of the hand. If

we discover that an articulation is strongly correlated

to another one then we can express the former in

function of the latter, reducing the necessary number

of myoelectric sensors but still maintaining our

purposes.

To measure the joint angles we used our hand

movement acquisition system developed by the

Health Involved Technical Engineering Group

(HITEG), at the University “Tor Vergata” (Saggio et

al., 2009). We limited the choice of gestures and

movements we believe to be the most useful for an

impaired person. We took the couple of joints that

showed the best correlation and we calculated, by

means of linear regression, the best approximation

that allow to infer the position of a joint with respect

to another one. It’s important to stress that

considering different sets of movements can lead to

different results (Vinjamuri et al., 2010).

2 THE DATA GLOVE

For our experiment we adopted the so called

HITEG-Glove as previous reported (Saggio et al.,

2009) and shown in Fig. 1. It is constituted by 18

sensors, placed according to Fig. 2. This data glove

has three sensors for each finger (3-14): one for

measuring the Metacarpo Phalangeal (MCP) angle,

one for the Proximal Interphalangeal (PIP) angle and

one for the Distal Interpahlangeal (DIP) angle, while

thumb is measured by only two sensors (1-2). There

242

Saggio G., Cavallo P., Casali D. and Costantini G..

COMPLEXITY REDUCTION IN CONTROL OF HUMAN HAND PROSTHESIS FOR A LIMITED SET OF GESTURES.

DOI: 10.5220/0003156902420247

In Proceedings of the International Conference on Health Informatics (HEALTHINF-2011), pages 242-247

ISBN: 978-989-8425-34-8

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

are also other four sensors to measure the angle

between the fingers (15-18). With the overall

acquisition system, the expected error in measuring

each finger joint position is as low as 4 degree.

Figure 1: HITEG Glove.

3 SET OF POSTURES

To perform a consistent reduction of the complexity

of the system we chosen a limited set of movements.

This choice strongly affects the correlations that will

be found in our analysis, and so it is very important

to make a good selection among the most common

and useful gestures. Missing some important

movements could lead to spurious correlations while

choosing useless movements that have no practical

utilization could unintentionally prevent some

possible reductions.

Figure 2: Position of the sensors over the hand

articulations.

Keeping in mind this concept and considering

that all transitions from a position to the next one are

recorded and included in the analyzed dataset, we

selected the positions discussed in the following

paragraphs and shown in figure 3. Note that we

excluded positions implying third and fourth finger

moving independently: these positions are

notoriously uncomfortable, usually avoided also by

healthy people, and have no real practical utility.

This exclusion will bring an obvious correlation

between last two fingers: if we want to give the

Figure 3: Hand positions from A to I.

COMPLEXITY REDUCTION IN CONTROL OF HUMAN HAND PROSTHESIS FOR A LIMITED SET OF

GESTURES

243

possibility to control separately these two fingers we

just have to discard this correlation, which in our

experiment is expressed by the couple 9-12: we will

just need eight sensors in spite of seven.

Data acquisitions were performed measuring the

nine basic movements described in the following,

repeated 10 times by 5 different healthy persons 25-

40 aged.

3.1 Position A: Open Hand

The open hand position is a fundamental position,

useful in different occasions and can be a transition

posture from one gesture to another.

3.2 Position B: Fist

Closing completely the hand in the fist posture, all

the fingers and the thumb are almost in the

maximum bent position. It is adopted, for example,

any time we want to keep something small in our

hand.

3.3 Position C: Index Finger Up

The index finger up position is the main gesture of

the hand: it is used every time we want to point

somewhere or somebody, or to press a button.

3.4 Position D: Index and Middle

Finger Up with Thumb Closed

This fourth position, with the index and middle

finger up with the other fingers bent.

3.5 Position E: Index and Middle

Finger Up with Thumb Open

In this posture the thumb and the first two fingers

are completely outstretched while the others are

bent.

3.6 Position F: Hand Open, with

Thumb Closed

This position represents the motion of thumb

independently, while all fingers remain outstretched.

3.7 Position G: OK Sign

This posture represents the gesture that we do, as an

example, to collect something with thumb and index

finger, maintaining the others opened. It differs from

the position used to hold a pen because the DIP of

the index in this gesture is bent.

3.8 Position H: Grabbing an object

This position is what we do to grab and hold an

object.

3.9 Position I: Holding a Pen

When holding a pen the DIP of the finger does not

bend while the thumb is almost closed and the other

fingers are relaxed.

4 STUDY OF CORRELATION

We asked every subject to repeat all the A-I postures

in sequence 10 times, so obtaining a corresponding

dataset of 450 x 14 sensors. For every couple of the

14 finger joint angles, we measured the Pearson

product-moment correlation coefficient, which is

expressed by the following formula:





,







, 











(1)

where cov(X,Y) is the covariance of the two random

variables X,Y that we are comparing, and

is the

standard deviation.

In table I we reported all the correlation

coefficients. Numbers indicate the joints as shown in

Fig 2.

It’s important to notice that if our aim is limited

to a specific application, the number of correlations

would be surely higher and the complexity achieved

lower. For example if we want to develop a

prosthesis capable just to grab and release objects

we could relate every DIP and PIP to their respective

MCP (e.g. angles 5 and 4 represented by angle 3).

An observation that we can do is that all joints

from last two fingers are very highly correlated: this

is clearly due to the fact that last two fingers always

move together, in particular MCP, PIP and DIP of

third finger (9, 10, 11) are correlated respectively

with MCP, PIP and DIP of fourth finger (12, 13, 14).

Moreover, different articulations of the same

finger are almost correlated: MCP is correlated with

PIP. this is valid for the first finger (0.990), third

finger (0.955) and fourth finger (0.986), but

correlation seems less strong in second finger

(0.832). Also PIP is correlated with DIP: this is

strongly visible in the second, third and fourth finger

but not in the index. We expected this result because

the DIP of the index can bend (e.g. in position H) or

not (e.g. in position I).

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244

Table 1: Correlation coefficient for every couple of joint angles.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 1

2 .649 1

3 .377 .672 1

4 .357 .644 .990 1

5 .429 .470 .889 .851 1

6 .074 .167 .605 .625 .571 1

7 .103 .225 .604 .623 .526 .832 1

8 .018 .293 .697 .703 .650 .862 .983 1

9 .088 .110 .319 .341 .362 .770 .546 .519 1

10 .166 .188 .312 .340 .272 .677 .530 .508 .955 1

11 .112 .310 .519 .546 .440 .754 .695 .698 .889 .957 1

12 .117 .107 .400 .406 .474 .778 .584 .585 .979 .943 .911 1

13 .104 .160 .357 .372 .400 .758 .591 .579 .987 .973 .933 .986 1

14 .022 .259 .451 .456 .505 .728 .638 .660 .928 .941 .952 .956 .973 1

A visual representation of the correlation can be

seen in Fig. 4-6, where the horizontal position of

every point represents the value of the first angle

considered (from 0° to 90°) and the vertical position

represents the value of the second angle. Each

reported point is placed in the degree Cartesian

diagram, representing the reciprocal position of one

joint with respect to another for each posture.

Fig. 4 represents a case of no correlation: angle 2

vs. 11 (DIP of the thumb vs. DIP of third finger).

Fig. 5 represents a case of high correlation (MCP vs.

PIP of fourth finger). Fig. 6 represents a case where

there is a little correlation (0.605) but not enough to

justify a reduction.

Figure 4: DIP of thumb versus DIP of third finger (2-11).

It’s important to notice that if our aim is limited

to a specific application, the number of correlations

would be surely higher and the complexity achieved

lower. For example if we want to develop a

prosthesis capable just to grab and release objects

we could relate every DIP and PIP to their respective

MCP (e.g. angles 5 and 4 represented by angle 3).

All joints from last two fingers are very highly

correlated: this is clearly due to the fact that last two

fingers always move together, in particular MCP,

PIP and DIP of third finger (9, 10, 11) are correlated

respectively with MCP, PIP and DIP of fourth finger

(12, 13, 14).

Figure 5: MCP vs. PIP of fourth finger (12-13).

Moreover, different articulations of the same

finger are almost correlated: MCP is correlated with

PIP. this is valid for the first finger (0.990), third

finger (0.955) and fourth finger (0.986), but

correlation seems less strong in second finger

(0.832). Also PIP is correlated with DIP: this is

strongly visible in the second, third and fourth finger

but not in the index. We expected this result because

the DIP of the index can bend (e.g. in position H) or

not (e.g. in position I).

COMPLEXITY REDUCTION IN CONTROL OF HUMAN HAND PROSTHESIS FOR A LIMITED SET OF

GESTURES

245

It can be noticed that the distribution in Fig. 5 is

roughly a line with a negative offset. This means

that the joint on the y axis started to move before the

one on the x axis. These kind of relations can be

analyzed in all diagrams to discover interesting and

more precise correlations among the joints.

Figure 6: MCP if first finger vs. MCP of second finger (3-

6).

5 REDUCTIONS

Basing on the study of the correlation on the

previous section, we identified seven couple of

variables that could be considered related, hence we

could express one in function of the other.

A high correlation means that a graph like Fig. 5

is very near to be a line, so it can be expressed by

the following equation:





=



++



(2)

where x

and y

are any of the couples of variables

that we considered for the i-th observation, while a

and b are coefficients that have to be evaluated in

order to have the best fit, finally

is the error.

By means of the linear regression (Fisher R.,

1925), we can minimize the quadratic error, and

obtaining the values for a and b:

=





, 









(3)

=



−



(4)

where cov(X,Y) is the covariance between X and Y,

is the variance of X,

is the mean value of X

and

is the mean value of Y. In table II we

reported, for every couple of variables, coefficients a

and b, as well as the mean quadratic error that we

obtain by substituting the real value with the value

extrapolated with our linear function.

Table 2: Linear regression coefficients and mean error.

Joint couple a b mean error [°]

3-4

-0.0016 1.0097 3.12

7-8

-0.0046 1.0353 5.05

10-11

0.0229 0.9041 8.43

13-14

0.019 0.9475 5.23

9-10

0.0605 1.050 9.84

12-14

0.0463 0.9963 7.67

9-12

-0.0074 0.9343 5.41

In Figs 7-8 examples of regression lines are

shown superimposed to the graph for 10-11 and 7-8

joints respectively, using the a and b coefficients in

table II.

Figure 7: PIP vs. DIP third finger (10-11) with regression

line.

Figure 8: MCP if first finger vs. MCP of second finger (3-

6).

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246

Referring to Table II, the estimated mean error is

in any case lower than 10°, value that is in any case

comparable to the overall 4° error of the adopted

acquisition system.

6 CONCLUSIONS

In this paper a statistical analysis has been carried

out to discover the correlations among 14 joint

angles in the hand on a restricted set of 9 static

postures, that we took as the most common and

useful. We found out that the values of seven joints

can be computed basing on the values of the

remaining seven, with an error lower than 10

degrees. This can lead to a important reduction of

myoelectric sensors, from 14 to 7, useful for driving

an artificial prostesys. This can be true for the most

part of applications when it is not requested a very

high degree of accuracy or a large number of DOF.

For example robots or drones remote controlled that

need high precision but few DOF could be driven by

a hand wearable device with a small set of sensors.

This research can also improve gesture recognition,

reducing the complexity of the problem and

improving the classification.

Vice versa, this work states a limit in hand

controlled devices: we cannot use all of 14 finger

joints to pilot a device with 14 DOF because some

of the joints are not independent.

Future investigations can be done; In fact it can

be carried out a similar study on the basis of

supposition of non linearity between the finger

joints, or it can be considered the relations among

three or more articulations

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GESTURES

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