PROBABILISTIC WORKPSACE SCAN MODES OF A ROBOT

MANIPULATOR COMMANDED BY EEG SIGNALS

Fernando Alfredo Auat Cheeín, Fernando di Sciascio, Ricardo Carelli

Institute of Automatic, National University of San Juan, Av. San Martin 1109-Oeste, San Juan, Argentina

Teodiano Freire Bastos Filho

Electrical Engineering Department, Federal University of Espírito Santo, Av. Fernando Ferrari 514, Vitória, ES, Brazil

Keywords: Brain Computer-Interface, Robot Manipulator, Probabilistic Scan Mode.

Abstract: In this paper, probabilistic-based workspace scan modes of a robot manipulator are presented. The scan

modes are governed by a Brain Computer Interface (BCI) based on Event Related Potentials

(Synchronization and Desynchronization events). The user is capable to select a specific position at the

robot’s workspace, which should be reached by the manipulator. The robot workspace is divided into cells.

Each cell has a probability value associated to it. Once the robot reaches a cell, its probability value is

updated. The mode the scans are made is determined by the probability of all cells at the workspace. The

updating process is governed by a recursive Bayes algorithm. A performance comparison between a

sequential scan mode and the ones proposed here is presented. Mathematical derivations and experimental

results are also shown in this paper.

1 INTRODUCTION

Brain Computer Interfaces have got a great impulse

during the last few years. The main reasons for this

growing are the availability of powerful low-cost

computers, advances in Neurosciences and the great

number of people devoted to provide better life

conditions to those with disabilities. These interfaces

are very important as an augmentative

communication and as a control channel to people

with disorders like amyotrophic lateral sclerosis

(ALS), brain stroke, cerebral palsy, and spinal cord

injury (Kubler et al.,2001, Wolpaw et al., 2002).

The main point of a BCI is that the operator is

capable to generate commands using his/her EEG

(electroencephalographic) signals in order to

accomplish some specific actions (Wolpaw et al.,

2002, Lehtonen, 2003, Felzel, 2001, Millán et al.,

2003). Thus, an operator using a BCI can control,

for example, a manipulator, a mobile robot or a

wheelchair (amongst other devices) without using

any muscle. The EEG frequency bands have enough

information to build an alphabet of commands in

order to control/command some kind of electronic

device (Ochoa, 2002). In this paper a BCI, which is

controlled through alpha waves from the human

brain, is used. Although the EEG signal

acquisition/conditioning, which is part of this BCI,

was developed in other work of the authors (Ferreira

et al., 2006), one of the objectives of this paper is to

illustrate its versatility, mainly in terms of the simple

algorithms used.

Event related potentials (ERP) in alpha

frequency band are used here. Such potentials are

ERD (Event Related Desynchronization) and ERS

(Event Related Synchronization), well described in

the following sections. This BCI has a Finite State

Machine (FSM) which was tested in a group of 25

people.

The main contributions of this paper are the scan

mode algorithms proposed to allow the user to

command a manipulator (Bosch SR-800), based on a

probabilistic scan of the robot’s workspace. The

workspace is divided into cells. Each cell contains

three values: its position

),( yx at the robot’s

workspace plane and a probability value. This value

indicates the accessibility of that element. Once a

particular cell is accessed, its probability is updated

based on Bayes’ rule.

Alfredo Auat Cheeín F., di Sciascio F., Carelli R. and Freire Bastos Filho T. (2008).

PROBABILISTIC WORKPSACE SCAN MODES OF A ROBOT MANIPULATOR COMMANDED BY EEG SIGNALS.

In Proceedings of the First International Conference on Biomedical Electronics and Devices, pages 3-8

DOI: 10.5220/0001048400030008

 SciTePress

This paper is organized as follows: a brief

description of the sequential scan mode of the

manipulator’s workspace is presented in section 2.

The probabilistic scan modes proposed are shown in

Section 3. Section 4 shows the results for a

Montecarlo experimentation, where the probabilistic

evolution of the whole workspace and of a specific

cell is presented. Section 5 shows the conclusions of

this work.

2 SEQUENTIAL SCAN MODE

As a brief introduction, the sequential scan mode of

the robot workspace developed in Ferreira et al.

(2006) is presented here.

The workspace is previously divided into three

main zones as it can be seen in Fig. 1. The system

iteratively scans from zone 1 to zone 3 until one of

them is selected by the user (using EEG signals).

Once it is so, the selected zone is scanned row by

row until one is selected. Once a row is selected, the

system scans cell by cell (switching columns)

iteratively inside the selected row. After a cell is

selected by the user, the robot reaches the position

given by that cell.

Figure 1: Main zone division at robot’s workspace.

3 PROBABILISTIC SCAN

MODES

The two probabilistic scan modes shown in this

paper are based on Bayes rule for updating

probability values of the cells at the manipulator’s

workspace. The scan modes are shown in the

following sections.

3.1 First Approach of a Probabilistic

Scan Mode

The first approach of a probabilistic scan mode

works as follows:

1. The workspace’s resolution is set to 72 cells and

can be easily changed, decreasing or increasing

this number. The workspace behaves as a pmd

(probabilistic mass distribution).

2. Each cell has its own initial probability. This

value can be previously determined by some

heuristic method (for example: if the BCI

operator is right-handed, then cells to the right of

the workspace will have higher accessing

probability than the ones to the left). However, it

is also possible to set all cells to a probability

near zero, in order to increase or decrease them

depending on the times they are accessed by the

user. In this work, the first case was adopted.

3. Let a and b be the higher and lower probabilities

cells respectively. Then, the workspace is divided

into three zones according to these values. Table

1 shows how division is made. Let

)|( GCP

the probability of cell

C given a group G to

which it belongs.

4. Every zone at the workspace is divided in three

sub-zones under the same philosophy presented

before. Each one of these sub-zones contains a set

of probabilistic weighted cells.

5. The scan mode proceeds as follows:

I. First, the zone with the highest probability

value at the workspace is highlighted. If that

zone is not selected by the operator, the

second highest probabilistic zone is

highlighted. If it is not selected, the highlight

passes to the third and last zone. The scan

keeps this routine until a zone is selected.

II. When a zone is selected, the highlight shows

first the sub-zone with the highest probability

inside the zone previously selected. The scan,

in this case, is exactly the same used in the

last step.

III. When a sub-zone is selected, then the scan

highlights first the cell with the highest

probability of occupancy. If it is not selected,

the scan passes to the next cell value. This

routine keeps going on until a cell is selected.

Once a position is selected, the probability

value of the cell, sub-zone, zone and complete

workspace is updated. The update of the

probabilities values is made by the Bayes’

rule.

As it can be seen, the number of cells that belong to

a sub-zone or a zone is variable. Then, the

organization of the zones at robot’s workspace is

dynamic. This allows improving the scan mode in

BIODEVICES 2008 - International Conference on Biomedical Electronics and Devices

order to access in a priority way to the most

frequently used cells.

The probability update of each cell at the

workspace is based on the recursive Bayes’ rule.

Once a cell is reached by the user, its probability

value changes according to (1).

Table 1: Workspace’s Zones Definitions.

highest probability cell

value

lowest probability cell

value

⎭

⎬

⎫

⎩

⎨

⎧

≤<−+ aGCPbabc

)|()(

zone 1: the set of all

cells which

probabilities are the

highest of the

workspace

⎪

⎭

⎪

⎬

⎫

⎪

⎩

⎪

⎨

⎧

−+≤

≤<

−

))(

(

)|()

)(

bab

GCP

zone 2: the set of all

cells which

probabilities are of

middle range

⎭

⎬

⎫

⎩

⎨

⎧

−

+≤≤ )

)(

()|(:

bGCPbc

zone 3: the set of all

cells with the lower

probability of the

workspace.

Let C be any cell at robot’s workspace and G a set

to which that cell belongs. Thus, the updating

algorithm is given by,

)|()|()|()|(

)|()|(

)|(

GCPCGPGCPCGP

GCPCGP

GCP

kkkk

−−

−

(1)

Though (1) is mainly used in very simple

applications (Thrun et al., 2005), it fits as an

updating rule for the purpose of this work.

Equation (3) can be re-written in (4), where a

scale factor was used.

)|()|()|(

GCPCGPGCP

kkk −

(2)

According to the Total Probability Theorem (Thrun

et al., 2005),

is the scale factor, which represents

the total probability of

)(GP . In (1),

)|(

GCP

k −

is the

prior probability of a cell given the primary set to

which it belongs at time

1−k .

)|( CGP

is the

transition probability which represents the

probability that a given cell C belong to a set G.

Finally,

)|( GCP

is the posterior probability -at

instant k- of the cell used given the zone to which it

belongs.

In order to make sense to the use of the recursive

Bayes algorithm, an initial probability value must be

given to all cells at the workspace.

Figure 2 shows the evolution of a cell’s

probability when it is accessed successively by the

user.

The cell used in Fig. 2, for example, has an

initial value of 0.05 but it is increased each time the

cell is accessed by the user. As was expected, the

maximum value a cell can reach is one. When this

situation occurs, the whole workspace is scaled. This

scaling does not change the scan mode because the

relative probability information remains without

changes, i.e., if a cell p has the maximum probability

over all cells, after scaling, p will continue being the

cell with the highest weight. A more extended

development of this algorithm can be seen at

Papoulis (1980). Once the updating algorithm is

complete, the scan algorithm is released as described

in Section 3.

0 20 40 60 80 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Probability Cell evolution

Numbers of iterations

Cell Probability Value

Figure 2: Evolution of Cell’s probability when

successively accessed.

0.5

Probability values of the workspace's cells

Prob abi li t y

0.5

Workspace primary zones

0.1

0.2

0.3

0.4

Figure 3: Probabilistic distribution of a workspace for a

right-handed user.

Figure 3 shows the workspace’s pmd for a right-

handed user. Fig. 3.a shows the cells probability’s

value and Fig. 3.b shows the different zones of the

manipulator’s workspace.

3.2 Second Approach

This second approach investigated in this work is

based on the sequential scan mode algorithm. Each

zone or sub-zone -as those shown in Fig. 1- has a

probability value associated with it. As the

workspace is considered as pmd then each zone or

sub-zone’s probability value is calculated as the sum

of all probability values of the cells that belong to

that group. The scan mode proceeds as follows:

The zone with the highest probability is

highlighted first; then, the second higher

PROBABILISTIC WORKPSACE SCAN MODES OF A ROBOT MANIPULATOR COMMANDED BY EEG SIGNALS

probability zone is highlighted and then the last

zone (see Fig. 1). The highlighting process

repeats until the user chooses a zone.

Once a zone is chosen, the row with the highest

probability -inside that zone- is highlighted. A

row of a zone is known as sub-zone. If this sub-

zone is not selected by the user after a period of

time, the highlight passes to the next higher

probability value row. This process is repeated

iteratively until a row is selected by the user.

Once a sub-zone is chosen, the cell with the

highest probability of that sub-zone is

highlighted. If it is not chosen after a period of

time, the highlight passes to the next higher

probability cell. The process continues and if no

cell is chosen, it starts from the beginning cell.

If a cell is chosen, then its probability is updated

according to the Bayes rule (Eq. 3). Then,

workspace pmf, sub-zone’s probabilities and all

zone’s probabilities are also updated.

The sampling time used in all scan modes is the

same one used in Ferreira et al. (2006).

4 EXPERIMENTAL RESULTS

This section is entirely dedicated to compare the

three scan types: sequential and probabilistic ones.

For this purpose, a Montecarlo experiment was

designed (Ljung, 1987). This experiment shows the

performance of the three methods by measuring the

time needed to reach different cells at the robot’s

workspace.

4.1 Montecarlo Experiment

The robot’s workspace consists of 72 cells. It also

can be considered as a

184

matrix. According to

this, a cell’s position is defined by a number of row

and a number of column at that matrix. The number

of a row and a column can be considered as a

random variable. To generate a random position of a

cell destination, the following algorithm was

implemented.

An uniform random source generates two

random variables:

and y .

ii.

The random variable

is mapped into the

rows of the

184×

matrix workspace.

iii.

The random variable y is mapped into the

columns of the

184×

matrix workspace.

iv.

When a position is generated, both scan

types begin. The time needed to reach the

cell is recorded.

After the system reaches the position

proposed, a next process point generation is

settled -the algorithm returns to point i-.

4.2 Mapping Functions

Let

f be a mapping function such as:

BAf

→

where,

[

)

{

}

{}{}

⎩

⎨

⎧

ℵ⊂∈=

ℜ⊂∈=

4,3,2,1:

1,0:

mmB

xxA

(3)

and let

be another mapping function such as:

CAf

→

where,

[

)

{

}

{}{}

⎩

⎨

⎧

ℵ⊂∈=

ℜ⊂∈=

18,...,3,2,1:

1,0:

nnB

yyA

(4)

Equations (3) and (4) show the domain and range of

the mapping functions. Finally, the mapping is made

according to the following statements.

Let

be the sum of all weights at robot’s

workspace, that is,

∑∑

∈∈

BiCj

, where

the probability value of a cell located at the

rowi

−

and columnj

−

ii.

Let Ax

∈

be an outcome of the uniform

random source for

f .

 If

∑

∈=

<≤

Cji

then

1)( == ixf

. This

means that the value of

Ax ∈ should be

lower than the sum of all cell’s values in row

one -over

- to )(xf

be equal to one.

 If

δδ

∑

∈=∈=

<≤

Cji

,2,1

then

2)( == ixf

This means that

∈

should be greater or

equal to the sum of all cell’s values in row

one and lower than the sum of all cell’s

values in row 2.

 The same process continues up to the last

row, whose expression is: if

δδ

∑

∈=∈=

<≤

Cji

,4,3

then

4)( == ixf

 Each time a cell is selected, the mapping

functions vary. It is so because they are

BIODEVICES 2008 - International Conference on Biomedical Electronics and Devices

dependent with the probability value of the

cells.

 For the mapping over the columns, the

procedure is the same, however in this case,

the sum is made over the set B (four rows).

Concluding, the mapping presented here is dynamic

because it is updated each time a cell varies its

probability value. For the case implemented in this

work (a right-handed user) the initial mapping

functions are represented in Figs. 4.a and 4.b. In Fig.

4.b is also possible to see that column 10 has higher

probability than column 1. It is also important to see

that, if all cells at robot’s workspace have the same

probability weight, then the mapping functions

would be uniform. Thus, each row or column would

have the same probability to be generated.

4.3 Montecarlo Simulation Results

The objective of Montecarlo experiments was to test

the performance of both scanning methods:

probabilistic and sequential ones. The performance

is measured in function of the time needed to access

a given position. This position is generated by the

uniform random source. After 500 trials the mean

time needed to access a random position by the first

approach of the probabilistic scan was of 20.4

seconds. For the second approach of the

probabilistic scan the mean time needed was of 16.8

and for the sequential scan was of 19.8 seconds. The

three results are in the same order but the

probabilistic second approach of the scan mode

requires less time. Consider now only the right side

of the workspace, which is, according to Fig. 3, the

most accessed side. The mean time of access for all

points belonging to the workspace right side is of 8.4

seconds under the first approach of the probabilistic

scan instead of 11.3 seconds corresponding to the

second approach of the probabilistic scan mode.

Under sequential scan, the mean time is of 14.8

seconds. The probabilistic scan mode first approach

is 43% faster than the sequential scan for cells over

the right side of the workspace while the second

approach is 23.7% faster.

0 1 2 3 4

0.2

0.4

0.6

0.8

app

unc

ues

Row value

Uniform Random Source

Figure 4.a: Mapping function for the four values of rows.

0 5 10 15

0.2

0.4

0.6

0.8

app

unc

umn

ues

Column value

Uni f or m Random Sour ce

Figure 4.b: Mapping function for the 18 values of

columns.

Figure 5 shows how a low probability valued cell in

the probability scan first approach evolves after

successive callings. The cell passes through the

different zones of cells according to its actual

probability value. After 240 iterations -or callings-,

the cell has passed through three zones and its

performance has also been improved as long as its

weight. In Fig. 5, one can see that at the beginning,

32 seconds were needed to access that cell.After 240

iterations, only 14 seconds were needed. This time is

smaller than the one needed on the sequential scan

mode which is of 18 seconds. Fig. 5 also shows

when the cell changes zones. Thus, if its probability

increases, the cell passes from, for example, primary

zone 2 to primary zone 1. Though a cell could be the

first in being scanned in the primary zone 2, if it

increases its value and passes to primary zone 1, it

could be the last scanned element in this zone. That

is the reason of the two time increments in Fig. 5. A

cell under the second approach of the probabilistic

scan shows similar behavior to the one showed in

Fig. 5.

20 40 60 80 100 120 140 160 180 200 220

Scan Mode Time evolution of a low Probability Cell after 240 iterations

Iterations

Time needed to reach the cell in secs

Cell under Probabilistic Scan

Cell under Sequential Scan

First Change of Zone

Second Change of Zone

Figure 5: Evolution of a cell access time.

Figure 6 shows the workspace state after 500

iterations generated by the Montecarlo experiment

using the first approach of the probabilistic scan.

Fig. 6.a shows the probability state of each cell at

the workspace while Fig. 6.b shows the new three

zones of the scan mode algorithm. One can see that

the non-connectivity tends to disappear.

PROBABILISTIC WORKPSACE SCAN MODES OF A ROBOT MANIPULATOR COMMANDED BY EEG SIGNALS

0.5

Probability values of the workspace's cells

Probability

0.5

Workspace primary zones

0.2

0.4

0.6

0.8

Figure 6: Workspace state after 500 iterations.

On the other hand, Fig. 7 shows the workspace state

after the same iterations of Fig. 6 under the second

approach of the probabilistic scan, though this scan

do not imply a dynamic behavior of the number of

cells of the different zones.

0.2

0.4

0.6

0.8

Probability values of the workspace's cells

Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Figure 7: Workspace state after 500 iterations under the

second approach of the probabilistic scan mode.

As it can be seen from Figs. 6 and 7, probabilistic

distribution of the workspace depends on the type of

scan mode used. Both probabilistic scan modes

presented in this work show a better performance

respect to the sequential scan mode.

5 CONCLUSIONS

The work presented here showed the implementation

of two probabilistic scan modes, based on a

recursive Bayes algorithm, of a robot manipulator’s

workspace. A comparison between these methods

and a sequential scan mode showed that the

probabilistic scan improves the access time of the

most frequently accessed cells. Although this system

could be implemented in several Human-Machine

Interfaces, it was primary designed for a Brain-

Computer Interface.

Experimental results show that the time needed

to access a specific position at the workspace is

decreased each time the position is reached. This is

so because the recursive Bayes algorithm

implemented updates the probability value of that

position once it is reached. A decrement of the

access time means that the user of the Interface

needs less effort to reach the objective.

In this work, a right-handed workspace

distribution case was presented. This case showed

that all cells to the right of the middle point -half of

the main workspace- have the higher probability and

the lower time needed to be accessed.

Finally, it is possible to say that the system learns

the user’s workspace configuration. It pays special

attention to those cells with the highest probability

minimizing the time needed to access them.

ACKNOWLEDGEMENTS

The authors thank CAPES (Brazil), SPU and

CONICET (Argentina) and FAPES (Brazil), for

their financial support to this research.

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