INDUSTRIAL APPLICATIONS VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
Fuzzy - Based Me hod o De ec ing he En i omen
Cha ac e o UAV Op ical S abiliza ion
Da id NOVAK1, Pe CERMAK2
1Ins i u e o Compu e Science, Facul y o Philosophy and Science, Silesian Uni e si y,
Bez uc Sq. 13, 746 01, Opa a, Czech Republic
2Resea ch Ins i u e o he IT4Inno a ions Cen e o Excellence, In i u e o Compu e Science,
Facul y o Philosophy and Science, Silesian Uni e si y, Bez uc Sq. 13, 746 01, Opa a, Czech Republic
oln[email p o ec ed], [email p o ec ed]
DOI: 10.15598/aeee. 13i3.1299
Abs ac . An op ical s abiliza ion o UAV (UAS) is a
e y impo an pa o a s uc u e in hei con ol sys-
ems. No only as a backup s abiliza ion sys em in a
case o IMU ailu e, bu also as a main sys em, used
o s abiliza ion o na iga ion. In his pape he con-
cep o a sys em o en i onmen cha ac e de ec ion is
p esen ed. The sys em can classi y a su ounding en-
i onmen depending on chosen cha ac e is ics. Such
sys em can be used o a be e ho izon de ec ion due
o swi ching o a co ec ho izon de ec ion algo i hm,
which can be used o de e mining he posi ion o UAV.
The sys em is based on Takagi - Sugeno uzzy in e ence
sys em and uzzy a i icial neu al ne wo ks. An ea lie
wo k on his subjec was p esen ed las yea , bu con-
cep o he sys em was edesigned wi h a usage o uzzy
a i icial neu al ne wo k o a mo e p ecisi e ou pu s
and au oma ic de e mina ion o cha ac e is ics o uzzy
se s on inpu .
Keywo ds
Fuzzy, IMU, in e ence sys em, ne wo k, neu al,
op ical s abiliza ion, UAV.
1. IMU and hei Weaknesses
1.1. Elec omagne ic Noise and GPS
Denied En i onmen
An ine ial measu emen uni (IMU) is an elec onic
de ice ha measu es and epo s a c a eloci y, o i-
en a ion, and g a i a ional o ces, using a combina ion
o accele ome e s and gy oscopes, some imes also mag-
ne ome e s. Cu en ly, he use o magne ome e s in
IMUs, is mo e common. Magne ome e s using changes
in he Ea h’s magne ic ield o mome emen de e -
mina ion. Magne ic ields a e ec o quan i ies cha -
ac e ized by bo h s eng h and di ec ion. Using hose
alues we can e alua e speed and accele a ion in 3D
space same way, like using accele ome e s. In a case o
an elec omagne ic in e ences, magne ome e p o ides
inco ec da a so e alua ions o posi ion a e inco ec .
Such IMU ailu e may cause an inco ec eac ion o
UAV con ol sys em and as esul c ash o damage o
a ehicle.
Elec omagne ic in e ences lead o an uncon olled
mo emen s o UAV in a case o algo i hm ailu e ( o
example posi ion hold). In such case, GPS signal can-
no be used o co ec ion due o low accu acy (usually
in me e s). D i o UAV, o example small helicop e ,
can lead o PID con olle oscilla ions which can cause
an uncon olled mo emen s in a ea o i e me e s and
mo e adius.
The mos common sou ces o elec omagne ic in e -
ence a e:
•UAV elec ic pa s - o example elec ic mo o s,
ansmi e .
•Magne ic anomalies - such as a s o m, elec ic
wi ing, elec ic ains.
•Elec omagne ic pulse, in en ional in e e ences.
Fo he easons men ioned abo e, he need o a
backup sys em is ob ious, especially o UAV. Unlike
no mal ai planes and helicop e s, which can be con-
olled by a human pilo in a case o senso ailu e, he
au onomous UAV do no ha e such an op ion.
c
2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 255
INDUSTRIAL APPLICATIONS VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
1.2. Op ical S abiliza ion o he UAV
The mos common al e na i e o IMU is an op ical s a-
biliza ion. Usually op ical low, co ne and ea u e de-
ec ion algo i hms a e used. Those algo i hms ha e
limi a ions especially due o he low esolu ion o on-
boa d came as. E en high esolu ion came as canno
p o ide enough usable da a in high al i udes. In such
al i udes, small changes and image shi ing, which a e
needed o op ical low de e mina ion, canno be de-
ec ed.
High al i udes o UAV and bad a mosphe ic condi-
ions a e easons o a ea u e de ec ion algo i hm ail-
u es. In such condi ions, image ea u es usually canno
be epea edly de ec ed. Fo applicable UAV op ical
s abiliza ion we need some ixed poin s (clus e s) o
de ec ed in o ma ion in cap u ed image. Such poin o
in o ma ion should be p esen in mos cap u ed images
so his in o ma ion can be used o de e mina ions o
mo emen s.
The ques ion is, how many poin s o in o ma ion is
needed o UAV s abiliza ion in 6 deg ees o eedom
(DOF). In ideal condi ion we ha e one de ec ed ea u e
o e e y deg ee o eedom. Fo backup sys em o IMU
i is possible o de e mine a comp omise and de ine
minimum numbe o such ea u es which we can use
o sho ime eme gency s abiliza ion.
2. Ho izon Based UAV
S abiliza ion
As a ho izon we can usually unde s and a di iding line
be ween sky and g ound. Usually we canno be su e
ha sky and g ound a e always isible, so le s use he
de ini ion o ho izon as he line, pa allel wi h wa e
su ace. Posi ion and angle o ho izon can be de e -
mined by human eye in mos o scanned images. The e
a e many de ec ion algo i hms o a ious condi ions.
P oblem occu s wi h only one onboa d UAV came a.
Usage o only one came a canno ensu e ha i will al-
ways cap u e he scene in which he ho izon is loca ed,
o he posi ion o he ho izon ha can be de e mined.
Such p oblem can be pa ially sol ed by usage o mo e
han one onboa d came a o wi h usage o pano amic
onboa d came a. In a case o bad a mosphe ic con-
di ions, which educes isibili y, we can use he mal
ision, UV o HR came a.
De ec ed ho izon p o ides in o ma ion, which can be
used o eme gency UAV s abiliza ion. F om ho izon
posi ion and angle we can calcula e in o ma ion abou
changes o pi ch and oll o UAV. In o ma ion abou
al i ude, o a ion and d i ing on ho izon al plane can-
no be de e mined. F om hose easons we need o add
an auxilia y image de ec ion algo i hms such as op ical
low and ea u e de ec ion.
The p oblem wi h low image esolu ion in high al i-
udes canno be e ec i ely sol ed. Bu p oposed s abi-
liza ion sys em will wo k as backup eme gency sys em,
so his p oblem may no be signi ican . In a case o
eme gency si ua ion we can p esume, ha scanned im-
age esolu ion will be g ea e when UAV is close o he
g ound o obs acle, so s abiliza ion sys em will ha e
mo e p ecise ou pu . Such ea u e can a oid collisions
in eme gency si ua ions.
F om in o ma ion abo e we can unde s and ha o
e icien op ical s abiliza ion, based on he ho izon de-
ec ion, we need o p o ide ce ain y o ho izon de-
ec ion in e e y si ua ion and en i onmen in which
UAV will ope a e. Such ea u e can p o ide p oposed
me hod o au oma ic en i onmen de ec ion.
2.1. Usual P oblems wi h he
Ho izon De ec ion Algo i hms
Cu en ly, he e a e some gene al ad ances in ho izon
de ec ion. Each o hem cande ec he ho izon unde
ce ain condi ions om he de ec ion o ho izon us-
ing Hough ans o ma ion o mo e complex me hods.
The e is an o e iew o some o he echniques and
p oblems depending on he condi ions in Tab. 1. In-
en ionally we do no men ion he de ec ion ho izon in
u ban a eas he e, because in such condi ions all lis ed
p ocedu es ail i ually.
The e a e a numbe o ho izons de ec ion solu ions
wi h di e en pe cen age success o he de ec ion. Fo
small UAVs, which each maximum heigh s o hund eds
o me e s, he ho izon de ec ion is no a i ial ask
hough. A his poin i is necessa y o de ine he di -
e ence be ween he ho izon and he isible ho izon.
We conside as he ho izon he di iding line be ween
sky and ea h, ha is, a ho izon al line ha is le el o
he g ound. We unde s and he isible ho izon as he
eal di iding line be ween sky and ea h, which is isi-
ble om a gi en loca ion in he scene. Visible ho izon
may he e o e no always be ho izon al wi h he g ound
plane. Ano he p oblem a ises na u ally in u ban a -
eas, whe e he ho izon mus be de ec ed o example
om anishing poin s o de ec ed building ou lines.
The ideal objec i e is o ind a uni e sal app oach
how o de ec he ac ual posi ion o he ho izon and
any en i onmen . Such p ocedu e would no ail in
any a ea, which he UAV can ge in.
To de ec ho izon in u ban a eas he e a e se e al
me hods ha a e based on he moni o ing o main lines
in he image and he de ec ion o he anishing poin s,
om which he likely posi ion o ho izon and i s angle
can be calcula ed.
c
2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 256
INDUSTRIAL APPLICATIONS VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
Tab. 1: Some p oblems o s anda d ho izon de ec o s depending on condi ions.
The me hod The bes esul s The possible weaknesses
Hough ans o ma ion,
edge de ec o s. G ea heigh s, s aigh ho izon. Fails a low al i udes
and inden ed a eas
Sea ching
o he cen e s o g a i y
o he g ound and sky.
Equally con ou ed ho izon In he inden ed su oundings
and a highe cloudiness
Op ical low. G ea heigh s, a li le con ou ed
ho izon.
May ail a low al i udes
and inden ed su oundings.
Algo i hms ha wo k wi h edges howe e ail in open
landscape, because he e is no co ec de ec ion o ho -
izon al lines and he subsequen de i a ion o he an-
ishing poin s because hey a e i ually absen in he
scene.
3. The De ec ion o he
En i onmen
Fo he p oblems desc ibed in he p e ious chap e s a
simple solu ion can be used, based on he idea o de-
ec ing he en i onmen , in which he UAV de ice is
mo ing, and he subsequen co ec choice o he al-
go i hm o de ec ing he ho izon. A his poin , i is
i ele an wha kind o algo i hms o ho izon ecogni-
ion we will use; he impo an hing is o choose a
leas one o landscape wi hou build-up a ea, one o
u ban a eas and one o indoo s. The ollowing pseudo-
code ep esen s he basic algo i hm o en i onmen
de ec ion.
Algo i hm 1
1: o e e do
2: i (de ec ed.en i onmen . a iable) < u ban
hen
3: e u n ho izon de ec ion algo i hm o open
en i onmen
4: else
5: i (u ban.en i onmen . a iable) < ou doo s
hen
6: e u n ho izon de ec ion algo i hm o u -
ban en i onmen
7: else
8: e u n ho izon de ec ion algo i hm o in-
doo s en i onmen
9: end i
10: end i
11: end o
Howe e , he choice o co ec algo i hm which co -
ec ly calcula es he decision a iables based on he
de ec ed pa ame e s, which will lead o he co ec en-
i onmen iden i ica ion is s ill a p oblem. Fo co ec
decision is be e o use some so -compu ing me hod.
We decide o use uzzy - based app oach. Basic p ob-
lem is, o cou se, selec ing he igh inpu pa ame e s.
3.1. The Choice o De ec ion
Pa ame e s
The in o ma ion lis ed in he ex abo e implies ha
one o he key pa ame e s o he decision-making al-
go i hm will be s aigh lines de ec ion and hei cha -
ac e is ics. Quan i y o de ec ed s aigh lines wi h
speci ic leng hs is qui e di e en in open scene y and
u ban de elopmen . Howe e , his may no always be
decisi e. The s aigh lines, which can p o ide alse
in o ma ion, such as loca ion o he anishing poin
(powe lines, ences, oads), can be de ec ed e en in
open landscape. The e o e, i is necessa y o p o ide
addi ional inpu pa ame e s. We mus include only
he lines ha ha e a ce ain leng h o he calcula ions,
hough. I is necessa y o exclude sho lines, which
may occu in bo h ypes o en i onmen s. We can se-
lec minimum leng h o s aigh lines using o example
he size o he p ocessed (see equa ion bellow), clong is
a cons an , which de ines he minimum size o he de-
ec ed lines.
seg =imagewid h +imageheigh
clong
.(1)
I is a good idea o use he di ec ion o de ec ed lines
o calcula e he nex pa ame e . I is speci ically he
numbe o lines ha ha e he same di ec ion as his a -
ibu e co esponds o a high deg ee o u ban en i on-
men . I is app op ia e o use he numbe o de ec ed
ec angles is he las pa ame e . I is essen ial o use
an algo i hm ha is able o de ec ec angles wi h pe -
spec i e [1]. Rep esen a ion o ec angles in he images
om u ban en i onmen is usually high. Because we
de ec he s aigh lines and hei di ec ions, he e is
no p oblem o ind he lines ha o m he edges o de-
ec ed ec angles. Fo de ec ion o en i onmen i is
necessa y o coun wi h he ac ha quad angles a e
also de ec ed ou side u ban a eas, bu hei numbe
will be low. Fo de e mina ion o a di e ence be ween
indoo s and ou doo s en i onmen we can use posi ion
o de ec ed anishing poin s. Le s sepa a e inpu se
o anishing poin s o wo g oups, inside image and
ou side. The e o e we ha e ou inpu pa ame e s:
c
2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 257
INDUSTRIAL APPLICATIONS VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
•numbe o line segmen s,
•numbe o pa allel lines clus e s,
•numbe o de ec ed ec angles,
•numbe o anishing poin s inside o image.
Ou pu pa ame e s o decision making a e h ee:
• a iable o u ban en i onmen ,
• a iable o non u ban en i onmen ,
•indoo a iable.
The inal ou pu om decision p ocess is classi ied
en i onmen (indoo , ou doo , ci y).
3.2. The P oposed Me hod
Fo sol ing his p oblem we can choose om many
possible so -compu ing app oaches. Fi s expe imen s
we e made wi h usage o uzzy Takagi - Sugeno in e -
ence sys em. Du ing implemen a ion o such sys em
some impo an p oblems occu ed. The bigges p ob-
lem was wi h uzzi ica ion o inpu and choosing a igh
uzzy se s o linguis ic a iables. uzzy se s had o be
speci ied manually, and ine uning also had o be made
by he p og amme . Also ules beha iou was no easy
o p edic . F om hose easons we decided o use an
a i icial neu al ne wo k wi h supe ised lea ning. Ou
sys em should be able o lea n om gi en examples o
en i onmen s. As he bes app oach seems o be us-
age o uzzy classi ica ion neu al ne wo k (NFC), which
app oxima es beha iou o Takagi - Sugeno in e ence
sys em [5].
Scheme o p oposed me hod can be seen in Fig. 1.
Images om onboa d UAV came a is p ocessed by im-
age ecognizing p ocedu es and numbe s o lines, clus-
e s, ec angles and anishing poin s a e de e mined.
Those alues a e used as an inpu o uzzy classi ica-
ion neu al ne wo k. Based on NFC ou pu , he co -
ec ho izon ecogni ion algo i hm is chosen. De ec ed
ho izon is used o u he op ical s abiliza ion o UAV.
Fi s s ep was o c ea e an Takagi - Sugeno based
uzzy in e ence sys em. A ypical ule in a Sugeno uzzy
model has he o m [3]:
Algo i hm 2
1: i Inpu 1 = x and Inpu 2 = y, hen
2: Ou pu is z = ax + by + ci
3: end i
Fo a ze o-o de Sugeno model, he ou pu le el zis
a cons an (a=b= 0). The ou pu le el zio each
Fig. 1: Scheme o p oposed sys em o en i onmen de ec ion
and s abiliza ion.
ule is weigh ed by he i ing s eng h wio he ule.
Fo example, o an AND ule wi h Inpu 1=xand
Inpu 2=y, he i ing s eng h is:
wi=AndMe hod (F1(x)F2(y)) ,(2)
whe e F1() and F2() a e he membe ship unc ions o
Inpu 1and Inpu 2. The inal ou pu o he sys em
can be he weigh ed a e age o all ule ou pu s.
FinalOu pu =Pn
i=1 wizi
Pn
i=1 wi
.(3)
Mo e abou he Sugeno uzzy in e ence sys ems can
be ound in [3] o [4]. Le us deno e he inpu and
ou pu pa ame e s as:
•SEG numbe o line segmen s,
•CL numbe o pa allel lines clus e s,
•RC numbe o de ec ed ec angles,
•VPI numbe o anishing poin s inside image.
Ini ial inpu uzzy membe ship unc ion we e se as
we can see on Fig. 2, we ha e chosen Gaussian unc ion.
Ou pu o in e ence sys em should be h ee a iables,
one o he u ban en i onmen , one o non-u ban en-
i onmen and one o indoo s.
Resul s om an ea ly expe imen s wi h he uzzy IS
can be seen on Fig. 3 and Fig. 4. We used he inpu pa-
ame e s wi hou anishing poin s de ec ion.URB and
NURB alues a e he uzzy IS ou pu s om ange
<0,1> and ep esen s de ec ed en i onmen membe -
ship. As we can see, he e we e p oblems wi h de-
ec ion o e lap, so he esul s we e no usable in eal
condi ions.
c
2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 258
INDUSTRIAL APPLICATIONS VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
Fig. 2: Gaussian inpu uzzy membe ship unc ion o p oposed
sys em.
0 5 10 15 20 25 30 35
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ou pu
alue
Ou doo s
URB
NURB
Fig. 3: Fuzzy IS o en i onmen de ec ion es ou pu (Ou -
doo s en i onmen ).
Many con igu a ions we e es ed, bu o eal wo ld
use we need mo e obus and eliable solu ion. F om
hose easons we choose o ap oxima e he uzzy IS
wi h a uzzy a i icial neu al ne wo k.
Nex s ep was o app oxima e uzzy IS wi h usage o
uzzy neu al ne wo k o classi ica ion (FNNC).
4. The Fuzzy Neu al Ne wo k
o En i onmen
Classi ica ion
Scheme o used FNNC can be seen in Fig. 5. As men-
ioned abo e, o i h ule, s h sample and j h ea u e we
a e using Gaussian membe ship unc ion wi h cen e c,
0 5 10 15 20 25 30 35
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ou pu
alue
Ci y
URB
NURB
Fig. 4: Fuzzy IS o en i onmen de ec ion es ou pu (Ci y
en i onmen ).
which is de ined as ollows [5]:
µij(xsj ) = exp −(xsj −cij)2
2σ2
ij !.(4)
Fo uzzy ica ion we a e using ollowing ule, whe e
Nis numbe o ea u es:
αis =
N
Y
j=1
µij(xsj ).(5)
De uzzy ica ion is done wi h usage o ollowing ule:
βsk =
M
X
i=1
αiswik.(6)
Weigh w ep esen ing deg ee o belonging o k h
class. Finally, de e mining o ou pu class C o s h
inpu is done simply by choosing he maximum:
Cs= max {osk}, k = 1,2, ..., K. (7)
Fo supe ised aining o he uzzy classi ica ion
neu al ne wo k we can use a ie y o lea ning algo-
i hms. Du ing he neu al ne wo k aining a cho-
sen algo i hm should upda e he alues o membe ship
unc ion cen e s and wid hs, also all weigh s on connec-
ion om uzzy ica ion o de uzzy ica ion laye . Usu-
ally a ian s o he SGG algo i hm is ecommended [5]
o aining howe e in his case we ha e p oblem wi h
a iable numbe o inpu s. Also he lea ning algo i hm
mus be able o wo k online. The main p inciple o
supe ised lea ning is o manual swi ching o co ec
en i onmen , which causes o gene a e designa ed ou -
pu . UAV now can collec da a and lea n om gi en
examples.
c
2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 259

INDUSTRIAL APPLICATIONS VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
Fig. 5: Scheme o uzzy neu al ne wo k o en i onmen classi-
ica ion.
A p esen , he online lea ning algo i hm o ou pu -
pose is he subjec o esea ch. Fo es ing unc ionali y
o p oposed sys em we a e using empo a y app oach,
which conside collec ing da a and hen make o line
lea ning. Those alues a e used as ini ial weigh s o
NFC. Nex s ep is o use modi ied online lea ning al-
go i hm, based on e o g adien descen p inciples.
5. Conclusion and Fu u e
Wo k
The abili y o de ec he cha ac e o he en i onmen
in which au onomous en i y ope a es should be an im-
po an ea u e o u u e au onomous sys ems, espe-
cially o UAVs. Usage o he uzzy classi ica ion neu al
ne wo k o such de ec ion is p obably an app op ia e
Fig. 6: En i onmen de ec ion applica ion sc een sho .
app oach as i co esponds o he cha ac e o he in-
pu pa ame e s ha ha e a high deg ee o unce ain y.
Also, his app oach seems o be app op ia e o he
possibili y o using he amoun o o line and online
lea ning algo i hms o uzzy neu al ne wo k.
Ou ecen esea ch indica es ha he me hod p e-
sen ed in his a icle is applicable o p ac ical use in
UAVs s abiliza ion sys ems. In he nea u u e we ex-
pec he publica ion o compa a i e esul s using di -
e en ypes o online o lea ning algo i hms and neu al
ne wo k con igu a ions.
Acknowledgmen
This pape has been elabo a ed in he amewo k o
he IT4Inno a ions Cen e o Excellence p ojec , eg.
No. CZ.1.05/1.1.00/02.0070 suppo ed by Ope a ional
P og am ’Resea ch and De elopmen o Inno a ions’
unded by S uc u al Funds o he Eu opean Union and
s a e budge o he Czech Republic.
We also like o hank SGS/8/2014 - Expe im-
age analysis and decision making in medicine and
UAS/UAV sys ems.
Re e ences
[1] SHAW, D. and N. BARNES. Pe spec i e ec an-
gle de ec ion. In: P oceedings o he Wo kshop o
he Applica ion o Compu e Vision, in conjunc-
ion wi h ECCV 2006. G az: Sp inge , 2006, pp.
119–127. ISBN 978-3540338345.
[2] NOVAK, D. and P. CERMAK. Ad an ages o
using mul i-agen p inciples in FAIL - SAFE
UAV sys em design. In: 16 h In e na ional Con-
e ence on Me hods and Models in Au oma ion
and Robo ics (MMAR). Miedzyzd oje: IEEE,
2011, pp. 162–167. ISBN 978-1-4577-0912-8.
DOI: 10.1109/MMAR.2011.6031337.
[3] PASSINO, K. M. and S. YURKOVICH. Fuzzy
Con ol. 1s ed. Columbus: Addison Wesley Pub-
lishing Company, 1997. ISBN 978-0201180749.
[4] TAKAGI, T. and M. SUGENO. Fuzzy iden i ica-
ion o sys ems and i s applica ions o modeling
and con ol. Sys ems, Man and Cybe ne ics. 1985,
ol. SMC-15, no. 1, pp. 116–132. ISSN 0018-9472.
DOI: 10.1109/TSMC.1985.6313399.
[5] DO, Q. H. and J.-F. CHEN. A Neu o-Fuzzy Ap-
p oach in he Classi ica ion o S uden s’ Aca-
demic Pe o mance. Compu a ional In elligence
and Neu oscience. 2013, ol. 2013, no. 6, pp. 1–
7. ISSN 1687-5273. DOI: 10.1155/2013/179097.
c
2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 260
INDUSTRIAL APPLICATIONS VOLUME: 13 |NUMBER: 3 |2015 |SEPTEMBER
Abou Au ho s
Da id NOVAK ecei ed his M.Sc. om Facul y o
Philosophy and Science, Silesian Uni e si y in 2010.
His esea ch in e es s include UAV/UAS au onomous
sys ems. He cu en ly wo ks owa ds his Ph.D. deg ee
unde he supe ision o Doc. Ing. Pe Ce mak, Ph.D.
Pe CERMAK was bo n in 1970 in
Opa a, Czech Republic. He g adua ed
om he VSB–Technical Uni e si y Os a a, ea ned
his Ph.D. in Technical Cybe ne ics. Associa e P o es-
so in he ield o Technical Cybe ne ics. In his ime
in Resea ch Ins i u e o he IT4Inno a ions Cen e o
Excellence, Silesian Uni e si y in Opa a and Di ec o
o Robo ic labo a o y. Main in e es s in Sys em Mod-
eling wi h using A i icial In elligence, Fuzzy-Neu al
Ne wo ks, Robo ics, Digi al Image P ocessing and
Analysis. Hobby in e es s in RC Helicop e , RC
ai planes and pho og aphy o na u e.
c
2015 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 261