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JOURNAL of AUTOMATION, MOBILE ROBOTICS& INTELLIGENT SYSTEMS

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If in doubt about the proper edition of contributions, please contact the Executive Editor. , excluding advertisements and descriptions of products.

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Articles2

JOURNAL OF AUTOMATION, MOBILE ROBOTICS

& INTELLIGENT SYSTEMS

VOLUME 6, N 4, 2012

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CONTENTS

Angle Measuring by MEMS AccelerometersKamil Zidek, Miroslav Dovica, Ondrej Liska

Modeling of Circulatory System with CoronaryCirculation and the POLVAD Ventricular Assist DeviceAlicja Siewnicka, Bartlomiej Fajdek, Krzysztof

Janiszowski

PI Control of Laboratory Furnace for Annealing of

Amorphous Alloys CoresJerzy E. Kurek, Roman Szewczyk, Jacek Salach and Rafa

Kloda

Surface Topography Parameters Important in ContactMechanicsPawe Pawlus, Wiesaw Zelasko, Jacek Michalski

Behavior Based Co-ordination of a Troop ofVehicles Targeted to Different Goals in an UnknownEnvironmentSourish Sanyal, Ranjit Kumar Barai, Pranab Kumar

Chattopadhyay, and Rupendranath Chakrabarti

About Evaluation of Multivariate MeasurementsResultsZygmunt L. Warsza

Positioning and Control of Nozzles and Water Particlesin Decorative Water Curtain and Water ScreensMahdi Hajiheydari, Sasan Mohammadi

Stable Gait Synthesis and Analysis of a 12-degree ofFreedom Biped Robot in Sagittal and Frontal PlanesA.P. Sudheer, R. Vijayakumar, K.P. Mohandas

Intelligent Utilization of Waste of Electrical and

Electronic Equipment (WEEE) with Robotized ToolJakub Szalatkiewicz, Roman Szewczyk

Influence of PWM to Trajectory Accuracy in MobileRobot MotionRyszard Beniak, Tomasz Pyka

Robot for Monitoring Hazardous Environments as aMechatronic ProductLeszek Kasprzyczak, Stanislaw Trenczek, Maciej Cader

Analysis of Influence of Drive System Configurationsof a Four Wheeled Robot on its MobilityMaciej Trojnacki

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Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME 6, N 4 2012

Articles 3

Angle Measuring by Mems Accelerometers

Kamil Zidek, Miroslav Dovica, Ondrej Liska

Submitted: 26thJune 2011; accepted 23rdSeptember 2011

Abstract:This article contains the description of MEMS acceler-

ometers implementation to device which is able to meas-

ure danger tilt. We can find out actual tilt in two basic

axes X and Y, from -90 to +90. Z Axis can only detect

fall of device or in vehicle system very fast downhill grade

during movement. For testing of the solution we select

small mobile robotic carriage. Hardware and software

part of solution are described. Because data from sensorare in raw format from analog MEMS Accelerometer, we

use free C# library with Kalman Filter implementation

to remove signal error. We can acquire next information

from sensor data for example movements trajectory in

X/Y axis (Cartesian system) and actual speed in all three

axes. Fast alarm is provided by RGB led diode (red color

is dangerous tilt.

Keywords: mems, Kalman filter, control.

1. Introduction to MEMS SensorsShortcut MEMS means micro electromechanical sys-

tems, marks mechanical and electromechanical construc-

tion of very small dimensions, and technologies used

for their preparation too. MEMS technology is based

on many tools and methods, which are used for creating

very small structure with dimension of couple microm-

eters. An important part of technology was takeover from

production of Integrated circuit (IC technology). Almost

all of these devices are based on a silicon substrate.

MEMS structures are realized from thin layer. There are

produced by photo lithographic methods. Some other

methods also exist, but they arent derivate straight from

technology of IC. There are three basic steps of operation

in MEMS technology for layer applying to silicon mate-

rial to substrate. Process of MEMS is usually a structured

sequence of this operation for creating real application.

Real device, then, contains central unit for processing of

data (microprocessor), and some other mechanical part

which compose unit named micro sensor too [4].

2. MEMS accelerometersOne of usual application for MEMS is sensor for

measuring of acceleration. This MEMS sensor is usually

named Accelerometer. They are divided to one-, two- or

three Axes. Measuring of acceleration is possible to use

in electronics and robotics for measuring: acceleration,deceleration, tilt, rotation, vibration, collision (crash) or

gravitation. Accelerometers are used in many devices,

special equipment and personal electrotechnics, for ex-

ample:

robots and automated devices with balancing func-

tion (segway),

controls with tilt measuring,

Auto pilots of aeroplanes,

car alarm systems,

car crash detection (used in airbag system),

monitoring of human movements (virtual reality

gloves).

Example of MEMS microstructure sensor magniedby microscope is displayed in Fig. 1 on the left side, right

is displayed measuring principle.

Fig. 1. MEMS sensor and principle of microstructures

Older accelerometers had big dimension and werevery expensive. The construction was created from stan-

dard metal parts, springs and PCB. That was reason why at

that time accelerometers were not used in electronics nor

robotics. This situation was changed thanks to progress in

MEMS technology. MEMS technologies reduce the price,

energetic consumption and dimensions. Main usability

is measuring of acceleration in three Axes: X forward/

backward, Y left/right, Z up/down. For mobile robot-

ics we can use this sensor for measuring acceleration or

deceleration by movement front and back, second Axis for

change direction of movement right or left, and third Axis

for fall detection of device. Second method of usability

is measuring of device tilt based on simple mathematics.

Figure 2 shows MEMS Axis conguration and principle of

tilt measuring with this sensor along y axis.

Fig. 2. MEMS sensor: axis conguration, principle of tilt

measuring

Output information from accelerometer is voltagewhich depends on movement or tilt of sensor in space.

A static characteristic of sensor is not exactly linear. For

common application we can this nonlinearity omit. The

acceleration is usually in MEMS application measured

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in G unit. Expression 1 g = 9,80665 m/s2 means, that

for every second, which passed the speed change will be

9,80665 meters for second. That is approximately speed

35.30394 km/h. The three Axis accelerometer can get

null G on every Axis, if is in ballistic trajectory known

as inertial or free fall. If we turn the accelerometer to

90 the output from one Axis will be exactly +1 g. In

this situation, accelerometer measuring gravitation Forceand can be in static position. Described characteristics for

analogue MEMS sensor is depicted in Fig. 3. [1]

Fig. 3. Characteristics of MEMS accelerometer sensor

with nonlinearity [2]

Example of block scheme sensor connection to user

application is displayed in the Fig. 4. Additional LCD

display connected straight to microcontroller enabling

testing of application without Computer necessity.

Fig. 4. Block scheme of complete application based on

MEMS accelerometer sensor

Sensitivity of measured values depends on sensor G

range (most precise we acquire if sensor is set to 1g). A

disadvantage is that we cannot measure the higher values

of acceleration. Common sensors are produced to 5g

and it is possible to switch between ranges during appli-

cation activity. Computations of tilt angles are realized

thru basic mathematics and goniometric function. V_out

is actual value of voltage; V_offset is voltage by 0 g. Sen-

sitivity of sensor is dened by technical documentation.

In math is necessary nd out positive or negative accel-

eration according to offset value. Datasheet math count

according this:

V_OUT=V_OFF+ V/g*1g*sin (1)

=arcsin(V_OUT- V_OFF)/(V/g) (2)

where:

V_OUT output of accelerometer (V) from ADCVOFF acceleration 0 g offset

V/g sensitivity

1 g world gravitation

tilt angle

Our values are counted according changed math,

because we dont know max and min values for actual

accelerometer. This math get extreme values during ac-

celerometer operation.

incr = 180 * (H_max - H_min) (3)

= incr * (H_nam - H_min) (4)

where:H_max, H_min initial value of accelerometer extreme

H_nam actual accelerometer value

3. Tested hardware platformIntroduced solution was tested on mobile com-

puter with open source application in programming

language C#. A prototype board contains Accelerom-

eter MMA7341L (analog) and accelerometer MMA7455

(digital) from Freescale. Currently there is active only

analog Accelerometer. Microcontroller computes values

of voltage for all Sensor Axis with help of three 10 bits

ADC converters. Data are coded to frames (9 bytes as

string $XXYYZZ1310). Every axis has value coded totwo bytes (Low and High 8 bites).

First method of accelerometer communication is only

for debug the application. Sensor is connected straight

to PC. Data are sent thru serial line to serial port of PC.

For implementation to mobile robot is used USART

interface without UART/RS232 Transducer and com-

municate straight with High Level control system based

on AT91 control board with Linux Embedded OS. These

serial data are transferred to TCP packet thru ser2net

command line application. Data are sent next thru wife

interface to C# application. Block diagram of testing de-

bug solution and mobile control system implementation

is displayed in Fig. 5. Figure 6 shows is rst prototype ofsensor without RS232/USB transducer.

Fig. 5. Block diagram of connection sensor to testing

mobile control system

Fig. 6. Hardware of accelerometer. 1 microcontroller;2 accelerometer MMA7341L (analog); 3 accelerome-

ter MMA7455 (digital); 4 voltage regulator LF33CDT;

5 I2C bus for LCD BO1602D; 6 USB connector; 7

RGB LED diode.

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4. Software platform implementationSoftware solution is based on an open source C# ap-

plication, which is currently implemented to mobile solu-

tion Graphical Interface of solution is displayed in Figure

7. Left is displayed 2D graphics, tilt in x-Axis, left 3D

graphics tilt in all three axis X,Y,Z. All values of real time

tilt are displayed in graphical interface in text edit boxes.

Basic value of danger tilt is set to value bigger than40. This value starts critical routine and block move-

ment of mobile device to actual direction. Danger tilt

value can be changed through graphical interface from

090.

Fig. 7. C# application, 3D tilt X,Y Axis and conguration

panel

5. Kalman flter implementation to smoothraw dataThe Kalman lter is an efcient recursive lter that

estimates the internal state of a linear dynamic system

from a series of noisy measurements. The Kalman lter

is used in sensor fusion and data fusion. Typically real

time systems produce multiple sequential measurementsrather than making a single measurement to obtain the

state of the system. These multiple measurements are

then combined mathematically to generate the systems

state at that time instant. Acquired data from MEMS sen-

sor are in raw form with many disturbances, white noise

etc. For testing solution we implement free C# Math.

NET Neodym (Signal Processing) [8] with Kalman lter

function to desktop application. Graphical interface pro-

vides settings of three basic values of Kalman ltering

r, T, q which is necessary for customizing lter for real

application.

r Measurement covariance

T Time interval between measurements

q Plant noise constant

Discrete Kalman Filter consists of two parts: predic-

tion and update.

prediction:

x(k|k-1) = F(k-1) * x(k-1|k-1) (5)

P(k|k-1) = F(k-1)*P(k-1|k-1)*F(k-1) + G(k-1)*Q(k-

1)*G(k-1) (6)

update:

S(k) = H(k)*P(k|k-1)*H(k) + R(k) (7)

K(k) = P(k|k-1)*H(k)*S^(-1)(k) (8)

P(k|k) = (I-K(k)*H(k))*P(k|k-1) (9)

x(k|k)=x(k|k-1)+K(k)*(z(k)-H(k)*x(k|k-1)) (10)

where:

S Measurement covariance,

K Kalman gain,

P Covariance update,

x State update,

F State transition matrix,

G Noise coupling matrix,

Q Plant noise covariance matrix,

H Measurement model,

R Covariance of measurements,I Matrix identify,

z Measurements of the system.

Figure 8 shows graph of actual values when MEMS

sensor is stand statically on the ground (blue plotline).

Black plotline shown ltered value cleared from errors

and noise from ADC transduction. There is used for test-

ing application only 1D Kalman lter for ltering only

actual acceleration value. Next extension will be imple-

mentation of 2D or 3D lter for all three Axes.

Fig. 8. Kalman ltering for raw accelerometer data in

static position

In the Fig. 9 is displayed data from accelerometer

during tilt to 90 to one side, next to static position andthen tilt to opposite side. Reference signal is red plotline.

Black line is Kalman ltered value.

Fig. 9. Dynamic data from MEMS Accelerometer sensor

with Kalman ltering

We experimentally nd out constants for kalman l-

ter with compromise of minimal displace during dynamic

and static operation: r = 30.0, T = 2.0, q = 0.1.

There is one problem in setup lter, when there is

very fast acceleration and deceleration. This situation can

occur when the real device fall or crash to the obstacle.We can avoid this situation by setting adequate value to

danger alarm tilt and implementation of obstacles sensor

detection (infra or ultrasonic) to mobile solution.

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Articles6

6. ConclusionIntroduced measuring solution is implemented to

mobile device. Actual possibilities are measuring of tilt

device 90 to 90. You can select bound angle for start

indication of danger device tilt with next visual or sound

alarm. We can improve precision data from MEMS sen-

sor by using 12 bit ADC but then is necessary change themicrocontroller. Next idea can be change of Accelerom-

eter with digital I2C output, which removes error gener-

ated by ADC conversion. We are computing next values

from acquired data for example: trajectory, deceleration,

average and actual speed.

Next work on this solution will be an implementation

of Kalman lter to program of MCU rmware and dis-

play actual angle value and alarm on LCD display. This

remove testing mobile computer from actual solution and

application will be small and compact device. This re-

searched accelerometer device will be used in rehabilita-

tion system as safety circuit to monitor extreme accelera-

tion and deceleration for fast action to stop device.

AcknowledgementsThe research work is supported by the Project of the

Structural Funds of the EU, Operational Program Re-

search and Development, Measure 2.2 Transfer of knowl-

edge and technology from research and development into

practice: Title of the project: Research and development

of the intelligent non-conventional actuators based on ar-

tificial muscles ITMS code: 26220220103

AUTHORSKamil Zidek*, Ondrej Liska, Miroslav Dovica

Technical University of Kosice, Faculty of mechanical

engineering, Department of Biomedical engineering au-

tomation a measuring, Koice, 042 00, Slovakia, kamil.

[email protected], [email protected], miroslav.dovica@

tuke.sk

*Corressponding author

References[1] Tuck K., Tilt Sensing Using Linear

Accelerometers, Application Note, AN3461, Rev

2, 06/2007.http://www.freescale.com/les/sensors/

doc/app_note/AN3461.pdf

[2] Clifford M., Gomez L., Measuring Tilt with Low-g

Accelerometers, Application Note, AN3107, Rev

0, 05/2005,http://www.freescale.com/les/sensors/

doc/app_note/AN3107.pdf

[3] What is MEMS Technology? https://www.

memsnet.org/mems/what-is.html, Online, cit.

8.2.2010

[4] Johnson C. D., Accelerometer Principles,Process

Control Instrumentation Technology, Apr 14, 2009,0-13-441305-9.

[5] Zidek K: Open robotics control system, Technical

University Kosice, Online, www.orcs.sebsoft.com

[6] Saloky T., Pite J., Vojtko I., Control systems design

with reliability dened in advance. In:Proceedings

of the 1st IFAC Workshop on New Trends, Design

of Control Systems, Smolenice, Slovakia, 7th10th

September 1994, pp. 404407.

[7] Zidek K., MEMS Accelerometer SVN, Google

code, 2010. http://code.google.com/p/orcs/source/browse/#svn/MEMS_Accelerometer_SVN2

[8] Christoph Regg, Math.NET Neodym 2008 February

Release, v2008.2.2.364, http://www.mathdotnet.

c o m / d o w n l o a d s / N e o d y m - 2 0 0 8 - 2 - 2 - 3 6 4 .

ashx?From=NeodymCurrentRelease

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Articles 7

Modeling of Circulatory System With Coronary

Circulation and the POLVAD Ventricular Assist Device

Alicja Siewnicka, Bartlomiej Fajdek, Krzysztof Janiszowski

Submitted: 26thJune 2011; accepted 23rdSeptember 2011

Abstract:This paper presents an application of a numerical pack-

age for modeling and simulation of human circulatory

system. The model includes a coronary circulation and

the parallel heart assistance. The cases of the simulation

of the proper and the pathology circulation conditions,

such as left or right heart failure are shown. A descrip-

tion of the coronary circulation system is presented and

obtained coronary sinus occlusion simulation results areincluded. An implementation of the whole package as a

part of PExSim application is contained. The identifica-

tion experiment for the ventricular assist device has been

described and different methods of the artificial ventricle

modeling are presented. An example of use of a fuzzy

logic to presentation the dynamics of the POLVAD de-

vice is also included. Advantages of developed simula-

tion platform are discussed.

Keywords: PExSim, modeling of the circulatory system,

modeling of the coronary system, modeling of the ven-

tricular assist device, POLVAD.

1. Introduction

The continuous development of technology enabled

for the more common use of its achievements in medical

applications. Therefore, in recent years many scienticprojects were run to allow the use of technology to save

human life and health. One of the biggest bio-engineer-

ing projects in Poland is the Polish Articial Heart Pro-gram, whose aim is to develop of the construction and

control algorithms for the heart assist device. Application

of the developed solutions requires accurate testing. For

this purpose the modeling methods are widely used. In

recent years some different models of the human circula-

tory system were developed, both numerical and physical

ones, for example electrical or hydraulic [1, 2]. All of

them are widely used to reproduce hemodynamic condi-

tions of circulation system. Besides this, they can be ap-

plied for the testing of medical devices such as the blood

pumps or assist devices. For this purposes also models of

the same new devices are created. This way the possibil-

ity of simulating of the inuence of the heart support canbe obtained without carrying out experiments on living

organisms. This paper contains description of the devel-

oped circulatory model with the possibility of connec-

tion of the simply models of the extracorporeal ventricleassist device. In our case, the main aim of development

the mathematical description of circulatory system was

to create a research platform, for general purpose, which

could be easily adopted to solve different problems. For

example it could be used for determination and testing

of a Polish Ventricular Assist Device (POLVAD) control

and diagnostic algorithms.

2. Model of the circulatory system

The main part of the developed research platform

is the mathematical model of the circulatory system. It

is based on the description proposed by Ferrari [3] and

implemented as a part of the PExSim application [4].This software consists of predened function blocks thatrepresent basic mathematical and logic relationships, dy-

namic and static elements or support an input and out-

put operations. The possibility of easy extension with

user-written objects makes it a exible tool that can beused for emulation of complex dynamic system. For the

simple and clear presentation of circulation system and to

ensure the ability of easy parameters changes, each of the

blocks is responsible for reproducing behavior of differ-ent part of human circulatory system. They are grouped

in Human Circulatory System library, which consists

such elements and systems as:

left and right ventricle (LH, RH), systemic arterial circulation (SAC),

systemic venous circulation (SVC),

pulmonary arterial circulation (PAC),

pulmonary venous circulation ( PVC).

The model is based on a Starling`s law [3], which de-

nes the conditions for a balance between the lling andejection characteristics of the ventricle. The basic rela-

tion is a function that makes it possible to calculate theventricular pressure [3, 5]:

0 max max

( ) ( )

( ) ( ( ) ( )) ( ( ), ( ), ( ))v v v v v v

k Vv t j Vv t

P t V t V t E f V t V t V t

A e B e C

=

+ + +

(1)

where: Pv(t) the ventricle pressure, V

v(t) the ventricle

volume, Vv0

the ventricle rest volume, Ev(t) the nor-

malized elastanse function, Emax

the maximum value

of the elastance (end-systolic), max( ( ), ( ), ( ))v v vf V t V t V t the

correction function dependent on the ventricle volume

and ejection rate, and A, B, C, j, k constant parameters.The values of the flows are calculated as the ratio of

the proper pressure difference and the vascular resist-

ance. The rest of the pressures values arecalculated asthe solution of the differential equation which defines the

pressure derivative as the quotient of the sum of flowsand the capacity of the system. In the PExSim modeling

platform, the simple model of ventricular assist device

(VAD), based on the ventricle activity description, was

added. The parameters values were adopted to ensure

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Articles8

work consistent with the theoretical data. The model ofthe ventricular assist device is included into the system

between the atrium and the arterial system, creating a by-

pass of the model of the natural ventricle. The mathemat-

ical equations in the circulation blocks were respectivelyadopted to join the parallel ventricle support. The proper

connection of all elements creates a complete model ofcirculatory system with the external assist device (Fig. 1).

Fig. 1. The circulatory model in PExSim application with

the parallel connection of ventricular assist device

A full description of structure and function of the

blocks one can nd in [6]. As a result of this work wereceived a useful tool, that yields an investigation of the

proper and pathological circulation conditions and the in-

uence of the ventricle assistance for the hemodynamicconditions. For example, Fig. 2 presents the inuence ofthe left heart support on the atrium (P

la) and arterial (P

as)

pressures.

Fig. 2. The modeled waveforms of the atrium (Pla) and ar-

terial (Pas) pressures for normal, pathological and patho-

logical with left ventricle assistance (LVAD) conditions

In the ventricular failure state the blood accumulates

in atrium causing the rise of the pressure volume. At the

same time the pressure in arteries is low due to insuf-cient stroke volume of the heart. In simulation we canobserve the reduction of the atrium pressure value and

increase of the arterial pressure as a result of left ventricle

support which conrms medical observations.

3. The coronary circulation model

The system described above did not contain the coro-

nary circulation model. As the extension of functionality

of the developed platform, the coronary circulation mod-

el was developed and included. This way a possibility of

simulating the caval occlusion was achieved. The applied

mathematical description is the combination of the mod-els proposed in [7] and [8]. The schematic representation

of this, as an analogy to electric circuit diagram, is shown

in Fig. 3. It was added to the mentioned PExSim applica-

tion as a new CC (Coronary Circulation) element.

The driving pressure for the coronary circulation

(Psqz

) is taken as a proportional to left ventricle pressure.According to this, the input values for the model are:

pressure values in aorta, left ventricle and right atrium

(Pil, P

lv, P

ra). The others pressures are obtained by the

equations:

( ) ( ) ( )lca il lca art P t P t R Q t= (2)

( )( ) ( )lcxlcx sqz

lcx

V tP t P t

C= +

(3)

( )( ) ( )ladlad sqz

lad

V tP t P t

C= +

(4)

0

( )( ) exp[ ( ( ) )]venven ven ven

ven

V tP t V t V

=

(5)

where:

Plca

the pressure in bifurcation of coronary arteries, Pil

the aortic pressure, Qart

the coronary arterial flow, Plcx

and Plad

the coronary capillaries pressures (lad left

anterior descending artery, lcx

left circumflex artery),

Rlca

the arterial resistance, Clcx

and Clad

the coronary

capillaries compliances, Vlcx

and Vlad

the coronary cap-

illaries volumes, Vven

the coronary veins volume, ven

, ,V

ven0 the parameters for venous compliance.

The coronary arterial ow value (Qart

) is obtained as a

sum of the capillaries input ows (Qlcx1

, Qlad1

). Input and

output ows are calculated based on pressures differenceand blood vessels volumes as follows:

ows in direction to the coronary capilares system

(PlcaPlcx, PlcaPlad, PvenPlcx, PvenPlad, PraPven):

1

1

( ) ( )( ) lca lcxlcx

lcx

P t P tQ t

R

=

(6)

Fig. 3. The electric analogue of the coronary circulation

system

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Articles 9

1

1

( ) ( )( ) lca lad lad

lad

P t P tQ t

R

=

(7)

2

2

( ) ( )( ) lcx venlcx

lcx

P t P tQ t

R

=

(8)

2

2

( ) ( )

( ) lad ven

ladlad

P t P t

Q t R

=

(9)

( ) ( )( ) ven raven

ven

P t P tQ t

R

=

(10)

where:

Qlcx1

and Qlad1

the capillaries input flows, Rlcx1

and Rlad1

the capillary resistances, Qlcx2

and Qlad2

the capillary

output flows, Rlcx2

and Rlad2

the capillary resistances,

Qven

the flow supplying the right atrium, Pra the right

atrium pressure, Rven

the coronary venous resistance.

ows in direction from the coronary capilares sys-tem (P

lca

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Articles 11

Determination of the coefcients is performed mostlyin an indirect way of parametric identication method.On the base of sampled data the discrete transfer func-

tions )( zGQoutVj are determined in such a way that the

modeled signal, )(~

kQout , where is the sampling step,should be as closely as possible to the measured one. We

get a description consisting of a vector of inputs to the

model v(k

), containing the signals measured in the re-spective moments of time, and the vector of unknowncoefcients of the investigated transfer functions.

( ) ( )Q k v k out

=

(22)

Vector of transfer function coefcients can be esti-mated using various methods, for example, by the small-

est sum of squared errors (LS). The dynamic model de-

termined in this way usually accurately reproduces the

dynamics of the process but is very local. This means

that the change of supply parameters makes it necessaryto re-selection transfer function coefcients. That why,

the fuzzy modeling is very useful method. For the samestructure of the system (22) vector of coefcients isdependent on some fuzzy variables, dened by member-ship functions. For example, separate models can be de-

termined for the value of low, medium and high value

of the fuzzy variable. The model is the weighted sum of

the partial models and the corresponding membership

function values. General fuzzy model can be determined

as a linear combination of several local models set for

the different intervals of membership function. Estima-

tion algorithms of partial models coefcient vectors aremore complex and require the simultaneous calculation

of the vectors for all the partial models. The basic dif-

culty is also the designation of the proper shape andnumber of membership functions. In our case, in order

to obtain a general description of the dynamic properties

of the device, as a fuzzyfying variables were used two

signals: output ow value Qout

and a set pressure differ-

ent P. The rst signal determines different valve states(Fig. 9a): positive ow (ejection, valve open), backwardow (closing of the valve) and the closed valve phase (noow). For the second variable the membership functionwas divided for three areas (Fig. 9b): low, medium and

high values of pressure.

Fig. 9 The membership functions for the fuzzy variables:

a) output ow value, b) pressure difference

As a result of the presented fuzzy modeling method

the nine partial models had to be determined. The mea-

surements were carried out for ve values of pressuredifference. For the estimation of the models the measure-

ment data for maximum, medium and low pressure dif-

ferential were used. To verify the obtained model, the re-

maining series were used. The sample waveforms of the

modeled and measured output ow are shown in Fig. 10.

Fig. 10 Sample measured and modeled ow waveform

for the verication data set

The estimated parametric fuzzy model reproduces

output ow value relatively well both, for the data onwhich he was appointed and the verication series. Ityields a good representation of the dynamics of the

POLVAD articial ventricle. The extended description ofthe fuzzy modeling applied to determine the assist device

model one can nd in [11].

5. Summary

The paper presents a new numerical library for mode-ling and simulation of human circulatory system with the

extension of coronary circulation model and possibility

of the parallel assist device connection. The main result

of the coronary model addition was to allow simulation

and verification of the influence of the left ventricle as-

sistance on the coronary flow conditions. The whole li-

brary was implemented as a part of PExSim application.

Modular construction of the plugin ensures flexibility

because it can be easily modified to solve different prob-

lems within modeling and support of the human circula-

tory system. The modeling methods of the ventricular as-

sist device were presented. We received an approximate

representation of the output flow value dependent on the

supply pressure. Method based on fuzzy modeling made

it possible to achieve better results. However, in the caseof even small modification of the device construction,

the measurements and the whole modeling procedure

will have to be carried again. Also, we do not receive the

direct dependence of the output signal from the power

supply parameters. Work on the determination of a bettermodel of the mechanical construction of the ventricular

assist device is still carried out. However, as a result ofpresented work we have the useful tool, which gives theopportunity to study functions of individual components

of the human circulatory system as well as the system aswhole. It enables a simulation of the proper and the pa-

thology circulation conditions, such as left or right heart

failure. Implemented model of the ventricle assist device

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Articles12

gives the opportunity for modeling the influence of the

heart assistance on the hemodynamic co

Acknowledgements

This work was partially supported by the NationalCentre for Research and Development (NCBiR) in Po-

land under Project Development of metrology, informa-tion and telecommunications technology for the prosthet-ic heart as part of the Polish Artificial Heart Program.

AUTHORSAlicja Siewnicka*, Bartomiej Fajdek, Krzysztof Jani-

szowski Warsaw University of Technology, Faculty of

Mechatronics,Institute of Automatic Control and Robotics,

ul. w. Andrzeja Boboli 8, 02-525, Poland,

E-mail: [email protected], b.fajdek@mchtr.

pw.edu.pl, [email protected]

*Corresponding author

References

[1] M. Korda, S. Leonardis, J. Trontelj, An electricalmodel of blood circulation, Medical and Biologi-cal Engineering and Computing, vol. 6, 1968, pp.449451.

[2] M. Sharp, R. Dharmalingham, Development ofa hydraulic model of the human systemic circula-

tion,ASAIO J., vol. 45, 1999, pp. 535540.[3] G. Ferrari, Study of Artero-ventricular Interaction

as an Approach to the Analysis of Circulatory Phys-

iopathology: Methods, Tools and Applications,Ph. D. dissertation, Consiglio Nazionale delle Ri-cerche, Rome, Italy.

[4] K. Janiszowski, P. Wnuk, A novel approach to theproblem of the investigation of complex dynamic

systems in an industrial environment,MaintenanceProblems, vol. 4, 2006, pp. 1736.

[5] De Lazzari C., Darowski M., Ferrari G., ClementeF., Guaragno M., Computer simulation of haemo-

dynamic parameters changes with left ventricle as-sist device and mechanical ventilation, Computersin Biology and Medicine, vol. 30, 2000, pp. 5569.

[6] B. Fajdek, A. Golnik, Modelling and simulation ofhuman circulatory system.,Methods and Models in

Automation and Robotics (MMAR), vol. 15, 2010,

pp. 399404.

[7] W. Shreiner, F. Neumann, W. Mohl, The RoleOf Intramyocardial Pressure During Coronary Si-

nus Interventions: A Computer Model Study,IEEE Transactions on Biomedical Engineering, vol.

37, 1990, pp. 956967.[8] K. M. Lim, I. S. Kim, S. W. Choi, B. G. Min, Y.

S Won, H. Y. Kim, E. B. Shim, Computationalanalysis of the effect of the type of LVAD ow oncoronary perfusion and ventricular afterload, The

Journal of Physiological Sciences, vol. 59, 2009,

pp. 307316.[9] A. Siewnicka, B. Fajdek, K. Janiszowski, Appli-

cation of a PExSim for modeling a POLVAD arti-

cial heart and the human circulatory system withleft ventricle assistance,Polish Journal of Medical

Physics and Engineering, vol. 16, no. 2, 2010, pp.107124.

[10] M. Stachura, Application of the PExSim packagein identication of multi-dimensional model of a

waste water treatment plant,Pomiary AutomatykaKontrola, vol. 55, no. 3, 2009, pp. 156159.

[11] K. Janiszowski, Fuzzy identication of dynamicsystems used for modeling of hearth assisting

device POLVAD,Pomiary Automatyka Robotyka,11/2010, pp. 9095.

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Articles 13

PI Control of Laboratory Furnace for Annealing

of Amorphous Alloys Cores

Jerzy E. Kurek, Roman Szewczyk, Jacek Salach, Rafal Kloda

Submitted: 29th May 2012; accepted: 21stJune 2012

Abstract:There are presented theoretical and practical aspects of

automatic control of resistive furnace for thermal anneal-

ing of magnetic cores made of amorphous alloys. Process

of annealing requires specific conditions both from the

point of view of temperature and its changes. Solutions

presented in the paper create possibility for low value of

error as well as fast achievement of set value.

Keywords:PI controller, resistive furnace, temperature

control.

1. Introduction

New soft magnetic materials amorphous alloys based

on iron, nickel and cobalt gives new possibilities for de-

sign of inductive components [1], magnetic field sensors

[2], magneto-mechatronic sensors [3], and heat transpor-

tation devices [4]. However, production of amorphous

alloys cores requires precise thermal relaxation (cores

annealing) [5]. This process is usually realized in 1 hour

in argon protective atmosphere in order to avoid quickcorrosion of cores surface. The relaxation improves cores

magnetic permeability and reduces its coercive force.

Thermal relaxation in amorphous alloys, if performed

correctly, enables fabrication cores with relative perme-

ability magnitude greater than 2106. This makes the

amorphous alloys one of the best magnetic materials,

with highest magnetic permeability.

This paper describes a control system for resistive

furnace for annealing of amorphous alloys cores in the

laboratory of Institute of Metrology and Biomedical En-

gineering, Warsaw University of Technology.

2. The furnace, measurement system andcontrol system equipment

The thermal relaxation process of cores is realized in a

small laboratory resistive furnace which mass is approxi-

mately 3 kg. The furnace has canal winding, installed

in chamotte corpus covered by thermal isolation with

mineral wool. Inside the furnace there is a long quartz

pipe with 40 mm diameter, which is filled by argon with

pressure slightly higher than atmosphere pressure during

the relaxation stage. Argon atmosphere protects the core

during relaxation process.

The relaxation process begins with heating the furnace

to the relaxation temperature. Then, there is inserted cap-sule with room temperature having inside the annealed

core and it is heated in the furnace during required time

in the relaxation temperature. The temperature of amor-

phous alloys cores relaxation is equal to 345C and the

relaxation time is equal to 60 minutes. When the relax-

ation is finished the capsule is taken out of the furnace

and it is cooled inside the cold part of the quartz pipe.

Therefore, also cooling in argon protective atmosphere

is performed.

The controlled output signals are the furnace tempera-

ture measured by thermocouple type K and then the cap-

sule temperature measured by thermocouple type J. Ther-

mocouples are connected with temperature transducersAR-580 of Apar firm. Temperature measured range is

from 0 to 500C and transducers output range is voltage

from 0 to 10 V. Both sensors have linear characteristics.

The furnace is powered by pulse wide modulation

power controller EJ1P50E of Carlo Gavazzi firm. Con-

trol output of the controller is voltage from 0 to 10 V and

full pulse control period is 3 sec.

The furnace, temperature transducers and power con-

troller are connected with PC computer by data acquisi-

tion card NI-USB-6361 of National Instruments firm.

The control of the furnace temperature is realized by

computer controller implemented on the connected PC

computer. The controller program was prepared using theLabView software and implementing the PI controller.

Block diagram of the laboratory furnace for annealing

of amorphous alloys cores with measurement and control

system is presented in Fig. 1, and the furnace laboratory

stand is shown in Fig. 2, where 1 capsule with core,

2 furnace, 3 quartz pipe, 4 temperature transducer,

5 argon inlet, 6 data acquisition card and 7 PWM

power controller.

PCComputer

Transducer

AR-580

Transducer

AR-580

Thermocouple

type J

Thermocouple

type K

PWM Power

ControllerResistive

Furnace

Annealed

CoreNI Card

USB-6361

Fig. 1. Block diagram of the installation for annealing

of amorphous magnetic cores

Fig. 2. Laboratory stand of furnace for cores annealing

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Articles14

3. Requirements of the control process

As mentioned before, the controlled process consists

of (i) heating stage of the empty furnace and (ii) core re-

laxation stage in the relaxation temperature. The control

input is a voltage of power controller and the output sig-

nal is in the first stage temperature inside the quartz pipe

and in the second stage the annealed core temperature.

For the furnace heating stage it is only required rela-tively short heating time and limitation of control input

magnitude and change speed because of furnace proper-

ties, step response time for the furnace is approximately

3 hours.

Then, for the annealing stage it is required

1. annealing temperature equal to 345C,

2. annealing temperature errors should be less than

5C,

3. time of core heating from temperature 320C

to 345C no longer than 15 min,

4. no overshoots in the core heating stage to 345 C.

The third requirement is rather important since usu-

ally annealing process starts in temperature 320C and ifcore stay too long in the annealing temperature but less

than required annealing temperature its properties are

different to the required ones.

4. Identication of control plant

Model of the furnace has been calculated based on step

response of the furnace for change of voltage of power

controller from 0 to 0.7 V in the form

0( )

1

=+

T sG s e

Ts (1)

where kis model gain, Ttime constant and T0time delay.In the identification we have found the following val-

ues of the parameters

k= 500 [C/V], T= 3450 [sec], T0= 840 [sec]

In Fig. 3 there are presented response of the furnace

and response of the model. It is easy to see that the calcu-

lated model is quite good.

It should be however noted that because relatively big

mass of the capsule with core (0.25 kg) with respect to

mass of the furnace (3 kg) insertion of the core in room

temperature approximately 22C into warm furnace with

temperature 345C really inuent temperature of the fur-

nace.

Fig. 3. Furnace step response: measured temperature

and model response

5. Control algorithm

Accordingly to the requirements indicated in Section

3, two stages of the process were identied: heating stage

and annealing stage. Considering step response time for

the furnace (which is approximately 3 hours) two control

algorithms were proposed:

1. linear control of the furnace heating stage, and

2. linear control for annealing of the core with nonlin-ear phase after insertion of capsule with core into the

furnace.

In both cases we have used PI linear controller

+=

sTksR

I

P

11)(

(2)

Settings of the controller were chosen based on the

calculated model (1) of the furnace. Calculating the set-

tings in such a way that overshooting of the process is

equal to zero, =0, one obtains [6]

0

0

0.6 0.0049, 0.8 0.5 2397 (s)= = = + =P I

Tk T T T

kT

Next, we have modeled control system [Fig. 4] with PI

controller and calculated settings.

Furnace

PI Controller+

+ +

Tz

u Tr

Fig. 4. Block diagram of furnace temperature control

system, T furnace temperature, u control input volt-

age, Tr reference temperature, z disturbance

Unfortunately, in the contradiction to setting base we

have obtained small overshooting for step change refer-

ence temperature Tr, Fig. 5. However, overshooting for

the disturbance which modeled insertion of capsule with

core into the furnace was quite small. Therefore, we have

decided to apply for control of the furnace the PI control-

ler with calculated settings.

0 5000 10000 15000 20000 25000 300000

100

200

300

400

500

t (s)

T(oC)

Tr

T

0 5000 10000 15000 20000 25000 30000-0.5

0

0.5

1.0

1.5

2.0

2.5

t (s)

U(

V)

z

u

Fig. 5. Furnace model control response with PI controller

PI controller has been used for control of the furnace

and core temperature for (i) shortening of the furnace heat-

ing and (ii) control of the furnace heating after insertion of

0

50

100

150

200

250

300

350

400

0 5000 10000 15000

T ( oC)

t (s)

model

measurements

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Articles 15

the capsule with core and (iii) control of the core tempera-

ture in the annealing process.

The nonlinear phase of control algorithm after insertion

of the capsule with core into furnace was as follows:

1. before insertion of the capsule with core automatic con-

trol was changed into manual control with constant

control input voltage,

2. after insertion of the capsule into furnace there was add-ed one triangle control input impulse with magnitude

0.6 V and time 600 sec (10 min) to constant control in-

put; the triangle input was designed based on practical

experiments and in the control process it was automati-

cally generated by the controller software LabView,

3. after the triangle impulse the control was changed from

manual mode into automatic mode with PI controller

with calculated settings but also with annealing core

temperature as the controlled output signal.

In the control we do not use PID controller because in

the control system we have quick measurement distur-

bances which generate quite big control input changes cal-

culated by PID controller since derivative action D of PIDcontroller implemented in the software has big dynamic

derivative gain.

6. Experimental results

Designed control system has been applied for control of

the furnace for annealing of cores in the Institute of Me-

trology and Biomedical Engineering of Warsaw Univer-

sity Technology. In Fig. 6 there are presented temperature

of the furnace, temperature of the core and control input

voltage obtained by PI controller and triangle impulse in

the insertion of capsule with core into the furnace. Con-

troller settings were as we calculated before.

It is interesting to note that the core temperature is lower

than the furnace temperature in the annealing process.

In the annealing process we have obtained maximal core

temperature error 2C. The core heating time from 320C

to 345C was 12 min, less than it was maximal allowed

value 15 min and annealing time in temperature equal to

345C was 60 min.

7. Concluding remarks

Proposed PI control system allows conducting an-

nealing process according to requirements quickly and

in the required temperature without overshooting and

without presence of operator, operator action was only

required for short time in the moment of insertion of cap-

sule with core into furnace.

In laboratory conditions the proposed control system

has shorten the annealing time about 70% comparing

with annealing process in the manual mode and also im-

proved quality of the annealing because less annealing

temperature errors. Moreover, the annealing was auto-

matic and no operator assistance was required.Presently we work on improving the automatic anneal-

ing process and shortening assistance of the operator.

The research on magnetic cores was founded in 2010-

2012 as a research project.

AUTHORS

Jerzy E. Kurek* Institute of Automatic Control and

Robotics, Warsaw University of Technology, Warsaw,

Poland, [email protected].

Roman Szewczyk Industrial Research Institute for

Automation and Measurements, Warsaw, PL 02-486, Po-

land.Jacek Salach and Rafal Kloda- Institute of Metrol-

ogy and Biomedical Engineering, Warsaw University of

Technology, Warsaw, Poland.


References

[1] OHandley R., Modern magnetic materials prin-

ciples and applications. John Wiley & Sons, 2000.

[2] Ripka P., Magnetic Sensors and Magnetometers.

Artech, Boston, 2001.

[3] Bienkowski A., Szewczyk R., The possibility of

utilizing the high permeability magnetic materials in

construction of magnetoelastic stress and force sen-

sors, Sensors and ActuatorsA113, 2004, p. 270.

[4] Kolano-Burian A., Kowalczyk M., Kolano R.,

Szymczak R., Szymczak H., Polak M., Magnetoca-

loric effect in Fe-Cr-Cu-Nb-Si-B amorphous materi-

als.J. Alloys Comp.vol. 479, 2009, p. 71.

[5] Biekowski A., Szewczyk R., Salach J., Kolano R.,

Kolano-Burian A., Influence of thermo-magnetic

treatment on magnetoelastic properties of Fe81S-

i4B14 amorphous alloy,Journal of Physics Con-

ference Series 144, 2009, 012070. (http://iopscience.iop.org/1742-6596/144/1/012070)

[6] Puaczewski J., Ukady regulacji z regulatorami typu

PID, Poradnik Inyniera Automatyka, WNT, War-

saw 1973, pp. 571635. (in Polish)

Fig. 6. Heating and annealing process with PI controller

and triangle impulse control input: a) furnace and core

temperature b) control input voltage

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Articles16

Surface Topography Parameters Important in Contact

Mechanics

Pawel Pawlus, Wieslaw Zelasko, Jacek Michalski

Submitted: 2012; accepted: 2012

Abstract:The random surface models are important to many sta-

tistical peak-based contact models of rough surfaces.

Statistics of 3D surface topographies and 2D profiles

are compared and their interrelationship examined for

generated and measured common random engineering

surfaces. The applicability of the spectral moments ap-

proach to random surface specification is checked. Pa-

rameters important in contact mechanics, like summitdensity, summit curvature and summit height obtained by

their definitions and predicted by the spectral moment

approach, as well as calculated directly from profiles are

compared. Also, the values of plasticity index are com-

puted using various methods. Good agreement is found

between theory and measurement.

Keywords: surface topography, contact mechanics,

spectral moments.

1. IntroductionAll engineering surfaces are rough and their descrip-

tion is important to the study of many interfacial phe-

nomena, such as friction, wear, electric al and thermal

contact resistance, etc. Surface topography is recognized

as being an important factor in determining the nature

and extent of contact. Because surfaces are rough, the

true area of contact, which is much smaller than the

nominal area of contact must support very large pressure.

Two types of parameters were advocated for contact and

wear prediction: parameters based on peak (summits)

and parameters based on plots of material ratio.

The pioneering contribution to this field was made by

Greenwood and Williamson [1], who developed a basic

contact model (GW model) of isotropic surface. Chang

et al.[2] put forward an elastic-plastic contact model for

rough surfaces on the basis of volume conservation of

plastically deformed asperities. These models have been

extended by many researchers. Parameters connected

with peak as peak radius, peak height and peak curvature

were used. These parameters are based on a 2D profile.

However the statistic of the areal (3D) surface and the

statistics of a 2D profile of the surface are not the same.

It is necessary to distinguish a peak on a profile from

a summit on the surface. A detailed comparison was made

by statistical approach. Rough surfaces were modeled as

two dimensional, isotropic, Gaussian random surface byNayak [3]. Dependencies between profile spectral mo-

ments and parameters important in contact mechanics

were also developed by Bushet al.[4]. They were pre-

sented by McCool [5]. Surface and profile measurement

and their resultant statistics were compared and their in-

terrelationship examined for several common engineer-

ing surfaces [6]. Good agreement was found between

theory and measurements over a large range of sampling

intervals. Yu and Polycarpou [7] compared the summit

density and summit radius obtained from numerically

generated isotropic Gaussian surfaces.

2. Connections between summit parametersand spectral momentsSpectral moments m

0, m

2and m

4can be obtained from

profiles. They are equivalent to the mean square height,

rms. slope square and second derivative of profile.

The areal (3D) surface summit density is given by [5]:

4

2

1( )

6 3=

p

mSpd

m. (1)

The mean summit curvature averaged over all summit

heights is [5]:

48

3 =

mSpc . (2)

The variance of the summit height is [5]:

2

0

0.8968(1 )= s

as m . (3)

The distance between the mean of the summit height

distribution and the surface mean plane is [5]:

04 mys =

, (4)

where:0 4

2

2

=am m

m. (5)

3. Calculation procedureIsotropic surfaces of Gaussian ordinate distribution

were generated, using the procedure developed by Wu [8].

Each surface of this type is characterized by correlation

distance (in which the autocorrelation function decays to

0.1 value) and standard deviation of height. In addition,

some measured isotropic Gaussian surface topographies

were analyzed. The values of their texture parameterStrwere higher than 0.8. These surfaces were measured by

stylus 3D Talyscan 150 equipment with nominal radius

of tip 2 m. The initial numbers of the measured points

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Articles 17

were between 401 x 401 to 601 x 601. The sampling in-

tervals were 5 and 10 micrometers. However in order to

decrease correlation length sampling interval sometimes

increased and the number of points was reduced. For

each of measured surfaces, the form was eliminated by

a polynomial of the 2nddegree. Digital filters were not

used. For each surface, parameter connected with sum-

mits were calculated. For areal measurements, the meanradius of each summitRwas computed as reciprocal of

mean arithmetic average curvature in orthogonal direc-

tions. Summit curvature was calculated on the basis of

three-point formula [9]. The summit identification is

a real problem. Usually surface point is a summit if its

ordinate was higher than ordinates of four or eight near-

est neighbors (see Figure 1). The second possibility was

accepted by the present authors. This criterion was based

on works of Greenwood [10] and Sayles and Thomas [6]

as well as our previous research.

Areal density of asperitiesSpd, standard deviation of

summits heights sand distance between the mean of as-

perity heights and that of surface ordinatesys(see Figure2) were obtained from their definitions directly from ar-

eal surfaces. The parameters characterized summits were

also determined on the basis of 2D profiles. Sets of paral-

lel profiles were obtained from measured surfaces and

average profile spectral moments m0, m

2 and m

4 were

calculated according to procedure presented in paper

[11]. Parameters characterized summits were obtained

using equations (1) (5).

It is also possible to estimate parameters characterizing

summits from profile peaks analysis (summits are local

maxima on the surface, as distinct from peaks, which are

local maxima on a profile). Therefore peak density, aver-

age peak curvature, standard deviation of peak heightsand distance between the mean of line of peak heights

and mean profile line were calculated for set of parallel

profiles and mean values were taken into consideration.

As recommended by Nayak [3] sum-

mit density was computed as square

of peak density multiplied by 1.2.

The well-known plasticity index

postulated by Greenwood and Wil-

liamson (GW) [1] in 1966 is wide-

ly applied in studying the contact of

rough surfaces. The basic assump-

tions were adopted in GW model:

asperities are spherical near their

peaks (summits),

there is no interaction between as-

perities,

Fig. 1. Various summit identications

Fig. 3. Modeled isotropic surface topography (a), prole from this surface (b)

a) b)

Fig. 2. Scheme of contact of two rough surfaces

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Articles18

only the asperities deform during contact,

all peaks (summits) have the same radiusR.

The contact between two rough surfaces is modeled

by contact of single rough surface with a smooth plane.

Figure 2 shows the geometry model of contacting rough

surfaces, zdenotes the height of asperity, d separation

of the surfaces measured from the summits mean plane,

but his the separation of the surfaces based on surfaceheights (ordinates). The plasticity index postulated by

Greenwood and Williamson was defined as:

'0.5( )=

sy s

E

H R, (6)

whereHis the hardness of the softer contacting materi-

als, and

2 2' 11 2

1 2

1 1( )

= +

n n

EE E

(7)

Eiand

i(i = 1, 2) are Youngs moduli and Poissons ra-

tios for the two contacting elements.

In this work the plasticity index wascalculated for various methods of com-

puting contact parameters. The following

material properties were selected (con-

tact of steel-on-steel elements)E1=E

2=

2.07 x 105MPa, Brinell hardnessH= 200

(1960 MPa), 1=

2= 0.29. These proper-

ties were also used in paper [2].

Figure 3 shows example modeled sur-

face M1 of correlation = 0.85 between

neighboring points and profile from this

surface.

4. Results and discussionThe results of calculations of selected

surface topographies are listed in Table 1.

Index smeans calculation of contact pa-

rameters from the areal (3D) surface, m

using profile spectral moment andp

basing on the profile peaks analysis. Sur-

faces 1-5 were modeled, 6-10 measured.

means average value of correlation

between neighboring points (ordinates)

obtained from 6 profiles.

It is evident from the analysis of the

simulated and measured surfaces that

high values of the parameter (not small-

er than 0.85) correspond to large errors

of summit density Spdprediction using

spectral moment approach. The errors

were bigger than 100%; summit density

was overestimated. So the error in ob-

taining summit density on the basis of

profile measurement can be large. For

values between 0.25 and 0.77 the devia-

tions of summit density was smaller than

10%; for non-correlated neighboring

points ( between 0.1 and 0.12) applica-

tion of spectral moments method causedunderestimation of summit density

errors were between 15 and 18%. For

high correlation between neighboring or-

dinates the errors of summit density was also high based

on profile peaks analysis. For the other cases application

of this method led to overestimation of density; howev-

er it was found that summit density should be equal to

square of peak density on profile, in this case the error of

summit density was smaller than 6% for the coefficient

not higher than 0.77.

Mean radius of summit curvature was accurately pre-dicted by spectral moments approach, independently on

the value. The errors were smaller than 10%, only for

highly correlated points case ( = 0.99) deviation was

24%. Estimated value was usually smaller than that

obtained by definition. However the analysis of profile

peaks led to overestimation of mean summit radius; the

errors were in the range: 1635%.

Relative difference between standard deviation of

summit height was usually smaller than 5% but not

higher than 10% when spectral moments approach was

used. Higher errors occurred for measured surface topog-

Table 1. Surface topography parameters and plasticity indices calculated using

different methods

Surface , m s, m Spd, 1/m2 R, m y

s, m

M1s

M1m

M1p

0.85 0.176

0.174

0.174

0.158

0.164

0.169

0.00104

0.00211

0.00231

157.6

161.5

208.3

0.17

0.15

0.07

1.85

1.84

1.64

M2s

M2m

M2p

0.4 0.176

0.174

0.174

0.132

0.137

0.152

0.000191

0.000187

0.000235

1024.5

976.6

1351.4

0.25

0.25

0.12

0.65

0.68

0.61

M3sM3

m

M3p

0.12 0.1760.174

0.174

0.1230.13

0.142

0.0000610.000052

0.000077

3076.52816.9

4000.1

0.2540.269

0.14

0.360.39

0.34

M4s

M4m

M4p

0.91 0.93

0.91

0.91

0.82

0.87

0.91

0.000232

0.00047

0.000531

177.3

176.8

232.5

0.70

0.56

0.28

3.92

4.04

3.61

M5s

M5m

M5p

0.65 0.93

0.91

0.91

0.81

0.83

0.87

0.000063

0.000061

0.000074

714.2

713.9

952.4

0.95

1.06

0.48

1.94

1.92

1.74

M6s

M6m

M6p

0.5 0.66

0.64

0.64

0.46

0.5

0.51

0.000046

0.000042

0.000052

1383.1

1220.2

1724.0

0.79

0.89

0.45

0.99

1.18

0.99

M7s

M7m

M7p

0.25 0.82

0.8

0.8

0.49

0.56

0.61

0.000026

0.000024

0.000029

1666.7

1538.4

2173.9

1.1

1.24

0.64

0.99

1.13

0.97

M8s

M8m

M8p

0.99 0.57

0.56

0.56

0.56

0.56

0.56

0.00038

0.00081

0.0007

436.7

333.5

512.8

0.134

0.15

0.061

2.07

2.44

1.91

M9s

M9m

M9p

0.77 2.28

2.23

2.23

1.78

1.81

1.99

0.000019

0.0000199

0.000022

714.2

746.3

833.3

3.17

3.07

1.75

2.88

2.84

2.82

M10sM10

m

M10p

0.1 1.07

1.05

1.05

0.64

0.69

0.79

0.000017

0.000014

0.000019

1897.5

1724.13

2380.9

1.45

1.72

0.83

1.03

1.15

1.05

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Articles 19

raphies. When the sparameter was calculated directly

from profile based on its peaks, the deviations were usu-

ally higher (up to 24%). Estimation of summit standard

deviation height on the basis of profile analysis using

2 applied methods led usually to overestimation of s.

For highly correlated points ( = 0.99) no difference was

found after application of three analysed methods. In this

case standards deviation of summit height was equal orvery close to standard deviation of ordinates.

When spectral moments method was used, the pre-

dicted ysdistance was higher than value obtained from

the analysis of simulated and measured surfaces for cor-

relation smaller than 0.77, however for larger values

it was usually smaller (except for M8 surface) but dif-

ferences were not higher than 20%. Calculation of the

ysparameter directly from the profile peaks caused its

underestimation (1.7-2.5 times).

Generally when spectral moments were used, good

agreement was found between the theory and the results

of the areal (3D) surface topography analysis except for

summit density which could be overestimated by theoryfor comparatively high values. However these param-

eters cannot be calculated on the basis of profile peaks

analysis; the errors were higher, particularly for theyspa-

rameter. Only summit density can be calculated without

large errors as the square of peaks density on the profile

when correlation between neighboring points was not too

high. Therefore when summit contact parameters are es-

timated from profile spectral moments, values higher

than 0.85 should be avoided.

Application of spectral moments method led to correct

estimation of plasticity index for modeled surfaces; the

errors were not higher than 8%. Differences were larger

for measured surfaces (up to 20%). However plasticityindex can be determined on the basis of profile peak anal-

ysis the errors were not larger than 10% and for meas-

ured surfaces they were smaller than those obtained after

using spectral moments approach. The reason of such

low deviations is that as a result of application of profile

peak analysis both sandRvalues were overestimated.

Decrease of correlation length causes increase in the

distance between the mean of asperity heights and that

of surface ordinatesysand decrease in standard deviation

of summit height s. Mean value of standard deviation

of ordinates is a little smaller than standard deviation of

height of areal surface; differences were a few percents.

5. ConclusionApplicability of the profile spectral moment approach

to areal random surface specification was checked. Good

agreement between the analysis of modeled and meas-

ured surfaces and theory was generally found. The er-

rors of calculation of parameter important for contact

mechanics after the analysis of profile peaks, particularly

for the distance between the mean of asperity heights and

that of surface ordinates ys, were higher than those af-

ter using profile spectral moments. However the errors

of computing the plasticity index on the basis of profile

peaks analysis was small, especially for small correlationbetween ordinates. Summit density can be overestimat-

ed by the profile analysis (using both applied methods)

for comparatively high correlation between neighboring

points . Therefore when summit contact parameters are

estimated from 2D profiles, values higher than 0.85

should be avoided. Summit density can be calculated

as the square of peaks density on the profile when sum-

mit was identified based on its eight neighbors for not

too high correlation between ordinates. Decrease in the

parameter by increase in the sampling interval caused

increase in the distance between the mean of asperity

heights and that of surface ordinates ysand decrease instandard deviation of summit height

s.

AUTHORSPawe Pawlus*, Jacek Michalski Rzeszow Univer-

sity of Technology, Faculty of Mechanical Engineer-

ing and Aeronautics, Al. Powstancow Warszawy 8, 35-

959 Rzeszw, Poland. E-mails: [email protected],

[email protected]

Wiesaw elasko - Upper-Secondary Technical School

Complex in Lezajsk, ul. Mickiewicza 67, 37-300 Leza-

jsk, Poland. E-mail: [email protected]


References

[1] J. A. Greenwood and J. B. P. Williamson, Contact

of nominally at surfaces, Proc. Roy. Soc. (Lon-

don), A295, 1966, pp. 300-319.

[2] W. R. Chang, I. Etsion and D. B. Bogy, An elastic-

plastic model for the contact of rough surfaces,

ASME Journal of Tribology, 109, 1987, pp. 257-

263.

[3] P. R. Nayak, Random process model of rough sur-

faces,ASME Journal of Lubrication Technology,93, 1971, pp. 398-407.

[4] A. W. Bush, R. D. Gibson and G. P. Keogh, The

limit of elastic deformation in the contact of rough

surfaces,Mech. Res. Commun.3, 1976, pp. 169-

174.

[5] J. I. McCool, Comparison of models for the con-

tact of rough surfaces, Wear, 107, 1986, pp. 3760.

[6] R. S. Sayles, T. R. Thomas, Measurements of the

statistical properties of engineering surfaces,

ASME Journal of Lubrication Technology, 1979,

101, pp. 409-417.

[7] N. Yu and A. A. Polycarpou, Extracting summit

roughness parameters from random surfaces ac-

counting for asymmetry of the summit heights,

ASME Journal of Tribology, 126, 2004, pp. 761-

766.

[8] J. J. Wu, Simulation of rough surfaces with FFT,

Tribology International, 33, 2000, pp. 47-58.

[9] D. J. Whitehouse, The digital measurement of

peak parameters on surface proles,Journal Me-

chanical Engineering Science IMechE, 20/4, 1978,

pp. 221-226.

[10] J. A. Greenwood, A unied theory of surface

roughness,Proc. Roy. Soc. (London), A393, 1984,

pp. 133-157.[11] J. I. McCool, Finite difference spectral moments

estimation for proles: the effect of sample spacing

and quantization error, Precision Engineering,

vol. 4, no. 4,1982, pp. 181-184.

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Articles20

Behavior Based Co-ordination of a Troop of Vehicles

Targeted to Different Goals in an Unknown Environment

Sourish Sanyal, Ranjit Kumar Barai, Rupendranath Chakrabarti, Pranab Kumar Chattopadhyay

Submitted 26thJanuary 2012; accepted 16thAugust 2012

Abstract:The issue of coordinated operation of multi-vehicle for

a variety of tasks is getting increasing attention day by

day and standing as a major research field due to their in-

creased capacity and flexibility they can offer as a team.

This paper presents a novel algorithm for multi-vehicle

navigation, based on exhaustive search to avoid a set

of randomly generated obstacles, predict the approxi-

mate position of other vehicles and thus keeping a safedistance to avoid collision and to maintain a formation

amongst them while targeted towards the assigned goals.

The proposed algorithm uses two optimizing functions

in deriving drive commands, direction and turning, for

a troop of vehicles. This particular algorithm is similar

to the artificial potential field (APF) method which is

widely used for autonomous mobile robot path planning

due to its simplicity and mathematical elegance. In this

work we have taken a behavior based reactive scheme

together with artificially generated perturbation as the

vehicles are running in a real time environment. Simula-

tions have been carried out for a group of four vehicles,

paired in two groups, approaching two different targetsavoiding eight randomly generated obstacles, and keep-

ing proper coordination between the members of intra

and inter groups. The effectiveness of the proposed ap-

proach has been shown by some simulation results.

Keywords: behavior-based collision avoidance, rando-

mized obstacles, multi-vehicle coordination, particle

swarm optimization.

1. Introduction

The challenge that a troop of multiple uninhabited au-

tonomous vehicles (UAVs) would be able to adaptively

react to their environment, whether known, unknown or

uncertain, and learn about their surroundings while fol-

lowing either an individual or a communal agenda is an

intriguing field of research. Achieving such a degree of

control and producing such sophisticated behavior re-

mains an elusive goal that demands considerable atten-

tion and this is inherently a complex task. The problem

of multi-vehicle coordination and control has been re-

ceiving an exquisite amount of attention during the past

few years due to critical importance of the field in wide-

ranging applications [8].In many practical applications of autonomous vehicles

multiple teams are to be used. Such teams have many po-

tential benefits, including faster completion through par-

allelism and increased robustness through redundancy.

Further, teams of vehicles can increase the application

domain of autonomous vehicles by providing solutions

to tasks that are inherently distributed, either in time, or

in space, or in functionality. Since the 1980s, researchers

have addressed many issues in multi-vehicle, or multi-

robot teams or automated guided vehicles (AGVs) [12],

such as control architectures, communication, task al-

location, swarm robots, learning [25]. A critical issue

in these mobile robot teams is coordinating the motionsof multiple vehicles interacting in the same workspace.

Regardless of the mission of the vehicles, they must be

able to effectively share the workspace to prevent inter-

ference between the team members. Solutions to the mo-

tion coordination problem are approached in a variety of

ways, depending upon the underlying objectives of the

vehicle team. In some cases, the paths of the robots are

explicitly planned and coordinated in advance, as might

be needed in a busy warehouse management application.

In other cases, planning is relaxed and emphasis is placed

on mechanisms to avoid collision, applicable for tasks

such as automated hospital meal deliveries. In yet other

situations, the robots could have mechanisms with littlepre-planning that focus on coordinating vehicle motions

in real-time using reactive, behavior-based, or control-

theoretic approaches, such as would be used in a convoy-

ing or formation-keeping application.

Existing work on multi-vehicle control focuses reced-

ing-horizon planning (an optimization method) and hier-

archical structures. The receding-horizon trajectory plan-

ner based on Mixed Integer-Linear Programming (MILP)

is capable of planning planner-based trajectories directed

to a goal [14,15,16]. The goal is constrained by no-fly

areas, or obstacles, and is free from leader-follower ar-

chitecture which is adopted by model predictive control

(MPC) [17]. Game-theoretic approach is also adopted by

different co-ordination schemes for decision making of

the multi-vehicle problem [18,19,20]. A disjoint path al-

gorithm for a reconfiguration of multi-vehicle was also

proposed [21]. A class of triangulated graphs for alge-

braic representation of formations have been introduced

to specify a mission cost for a group of vehicles [22].

The present work focuses on simultaneous movement of

a troop of vehicles from their initial locations towards

different targets in such an environment where obstacles

are generating stochastically based on the Artificial Po-

tential Field (APF) approach. The basic idea of the APF

approach is to fill the robots workspace with an artificialpotential field in which the robot is attracted to its target

position and is repulsed away from the obstacles [4]. This

method is particularly attractive because of its elegant

mathematical analysis and simplicity. The application of

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Articles 21

APF for obstacle avoidance was first developed by Kha-

tib [3]. In the past decade this method has been studied

extensively for autonomous mobile robot path planning

by many researchers [5-7].This is a new approach where

the troops are divided into two groups and set out for

their own targets, maintaining a formation amongst them.

This work is an extension of the work done by KevinPassino [2] on obstacle avoidance of a single vehicle in

presence of a number of fixed obstacles.

2. Problem description

A. Cooperation of multi-vehiclesThe word cooperation means interaction or integra-

tion of multiple vehicles [11]. In a cooperative team the

vehicles have to communicate, exchange information or

interact in some way to achieve an overall mission. The

term cooperation has been widely discussed in different

scientific community and different definitions have been

proposed.

B. Multi-vehicle path planning problemIt is defined as follows: given a set of mvehicles in

k-dimensional workspace, each specified with an initial

starting configuration (e.g., position and orientation) and

a desired goal configuration, determine the path each ve-

hicle should take to reach its goal, while avoiding colli-

sions with obstacles and other vehicles in the workspace.

More formally, let A be a rigid vehicle in a static work-

space W =k

[18,19], where k = 2 or k = 3. The work-

space is populated with obstacles. A configuration q is

a complete specification of the location of every point on

the robot geometry. The configuration space C represents

the set of all the possible configurations of A with respectto W. Let O W represent the region within the work-space populated by obstacles. Let the close set A(q) Wdenote the set of points occupied by the vehicle when it

is in the configuration qC. Then, the C-spaceobstacle

region,obs

C , is defined as [1]:

{=obsC q | ( ) C A q } (1)

The set of configurations that avoid collision (called

thefree space) is:

\=free obs

C C C . (2)

Afree pathbetween two obstacle-free configurations

initC and goalC is a continuous map:

[0,1] freeC (3)

such that (0) = initc and .(1) = goalc .For a team of m vehicles, define a state space that con-

siders the configurations of all the robots simultaneously:

1 2 ...= mX C C C . (4)

Note that the dimension of X is N, where =N1dim( )

=m i

iC The C-space obstacle region must now be

redefined as a combination of the configurations leading

to a robot-obstacle collision, together with the configura-

tions leading to vehicle to vehicle collision. The subset

of X corresponding to robotiA with the obstacle region

O, is

{ | ( ) }= i i iobsX x X A q (5)

The subset of X corresponding to robot Ai in collision

with robotjA is

{ | ( ) ( ) }= ij i i j iobsX x X A q A q (6)

The obstacle region in X is then defined as the combi-

nation of Equations (5) and (6), resulting in

1 ,

( ) ( )=

= m

i i

obs obs obs

i ij i j

X X X (7)

With these definitions, the planning process for multi-

vehicle system treats X the same as C, andobs

X the same

asobs

C ,whereinit

C represents the starting configuration of

all the robots, and goalC represents the desired goal con-

figurations of all the vehicles.

The APF uses two types of potential field, namely a re-pulsive potential field to force a robot away from obsta-

cles or forbidden regions and an attractive potential field

to drive the robot to its goal. The rob

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