Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/3.
Na iga ion o di e en ial d i e mobile obo on
p ede ined, so wa e designed pa h
Á on Papp
Technical Ins i u e, Facul y o
Enginee ing
Uni e si y o Szeged
Szeged, Hunga y
pappa [email protected]
D . László Szilassy
Gamma Digi al K .
Budapes , Hunga y
szilassy.laszlo@gmammadigi al.hu
Józse Sá osi PhD
Technical Ins i u e, Facul y o
Enginee ing
Uni e si y o Szeged
Szeged, Hunga y
[email p o ec ed]-szeged.hu
This pape will be p esen ing he p ocess o mobile obo
mo emen con olling, om he ask o collec ing senso da a
un il he p oblem o con olling da a o he se o mo o
con olle s. In de ails, he i s pa will show he mechanism o
con e ing CAD da a o ou es, and he p ocessing o he
na iga ion da a ead om he senso s and calcula ed om
o me con olling commands. The second pa will explain he
p ocessing o na iga ion da a, he applying o he ac ual obo
posi ion and o ien a ion on he p ede ined i ual pa h and he
p oduc ion o he con olle 's inpu a iables. The Fuzzy
con olle and he ule base will be in oduced in he hi d pa .
Keywo ds — mobile obo , di e en ial d i e, obo na iga ion,
lase na iga ion, Fuzzy con ol, pa h planning
I. INTRODUCTION
Au oma ion o logis ic p ocesses has been made a
conside able p og ess in he ecen decades. One o he mos
equen ocuses o hese de elopmen s can be linked o
wa ehouse au oma ion-pa icula ly high bay wa ehousing,
palle anspo ing and he use o pneuma ic a i icial muscle
ac ua o s, especially alongside he so ing p ocesses- as
expe ienced while examining di e en esea che - and
s uden -p ojec s ([1], [2], [3], [4]).
This pape will ocus on con olling a di e en ial d i en
wo-wheeled obo on a p ede ined pa h, which has he
ollowing p e equisi es:
 Planning he pa hs, which he obo can d i e on, and
make he da a eady o use by algo i hms. In his case
he pa hs will be designed in Au oCAD, and hen
con e ed o a di ec ed, weigh ed g aph.
 Collec ing in o ma ion abou he obo ’s cu en
posi ion, and he ela i e angle o i s eloci y ec o .
 Calcula ing inpu da a o a Fuzzy con olle using
he cu en posi ion and he pa h-da a.
 Feeding he p econ igu ed con olle wi h he
calcula ed da a, and eading ou he e u n o he
Fuzzy con olle .
The con olle ’s ou pu s can be used o di ec ly con ol he
obo ’s d i e ain, in he cu en case he wo wheels o he
di e en ial d i e mechanism.
Re e ences [5], [6] and [7] ha e been used du ing he
design o he abo e de ailed con ol ci cle.
II. PATHPLANNING
A. Reading oom's con ou
A e s udying a ious me hods o obo na iga ion ([8],
[9]) o inding ou he obo ’s ac ual posi ion he decision was
made on he Sick NAV-350 lase senso - as in many o he
obo ics and AGV p ojec s so a ([10], [11]).
As a Ligh De ec ion and Ranging senso i is capable o
e u n he a ay o dis ances measu ed a e a 360 deg ee
e ical scan o he oom. An example scan esul can be seen
on Fig. 1.
Fig. 1. The oom's ho izon al con ou
B. Designing he allowed pa h’s
The con ou will be impo ed o an Au oCAD d awing,
whe e he use can c ea e he ou es allowed o he obo o
use.
Wi h special hanks o he ollowing companies:
Gamma Digi al K .
Sick É ékesí ő és Szolgál a ó K .
Technomed O osi Műsze gyá ó K .
Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/3.
The ou e consis s o LINE and SPLINE objec s, a
special use -de ined „STATION” objec , and he pe mi ed
d i ing di ec ion o he sec ions. The SPLINE objec s a e la e
con e ed o POLYLINE’s using he Au oCAD’s buil in
unc ion o his con e sion, as la e i will be easie o handle
a se ies o poin s, han a mixed se con aining poin s and
cu es. Fig. 2 shows he esul o con ou scan ex ended wi h
he abo e named pa h objec s.
Fig. 2. The con ou ex ended wi h ou e-objec s
III. PROCESSING THE AUTOCAD MODEL
The model will be expo ed as a .dx ile, which will be
p ocessed by algo i hms. In he cu en p ojec an open-sou ce
dx manipula o lib a y – dx lib – has been used o pa se he
model.
The ollowing s eps ha e been implemen ed o pe o m he
p ocessing ask:
 The i s phase is o collec he sec ions om he ile,
by s o ing he lines’ endpoin s in o an a ay.
 Second phase is o ind adjacen sec ions, which can
o m a con inuous pa h o he obo . Besides
compa ing he endpoin s o he linea sec ions, he
wo adjacen sec ion’s ela i e angle mus be 0 o π,
as well.
 Thi d phase is o ind and sa e he special
“STATION” endpoin s, which can be used as goal
posi ions.
 Fo h phase calcula es he leng h o all he sec ions.
 The i h phase ex ac s he pe mi ed di ec ion o
each sec ion.
A his s age a di ec ed, weigh ed g aph is a ailable o
sea ching he sho es pa h om he obo ’s cu en posi ion o
a desi ed place. As he map is s o ed using coo dina es o a
se ’s edges, he en i e map can be kep in he memo y
consuming only ew kiloby es (o megaby es o eally
complex cases).
IV. CALCULATING THE ROUTE TO THE GOAL
A. Finding he nea es sec ion o he obo
I is elemen a y o supe pose he obo a a pe mi ed
posi ion o e a sec ion. The dis ance o a poin o a line can be
calcula ed by subs i u ing he poin 's coo dina es o he
equa ion o he line, making i s absolu e alue, han di iding i
by he squa e oo o he sum o he squa es (1).
| |
√
(1)
Equa ion (1) can only be used o lines, bu no o
sec ions, since i is necessa y o de e mine he place whe e he
pe pendicula is in e sec ing he line (which is con aining he
segmen ).
A––––––––––––––P–––––––B
|
R
Fig. 3. Calcula ing he obo 's dis ance o he segmen s
On he Fig. 3 poin A and poin B a e ep esen ing he
sec ion endpoin s, poin R is he obo 's cu en posi ion, and
poin P is he place, whe e he pe pendicula s a ed om R
ha e in e sec wi h he sec ion. Using he do p oduc o he
ec o s AB and AR, he placemen o he in e sec ion can be
calcula ed. I he esul is less han ze o, he in e sec ion is
be o e poin A, and i he esul is g ea e han he leng h o
AB, he in e sec ion is a e he B poin .
Using a no malized o m o he calcula ion explained
abo e allows de e mining he coo dina es o he poin P, as
shown in (2), (3) and (4).








‖




‖
(2)
(3)
(4)
The alue o „ ” indica es he loca ion o he poin P along
he AB sec ion:
 = 0 : P = A
 = 1 : P = B
 < 0 : P is on he backwa d ex ension o AB
 > 1 : P is on he o wa d ex ension o AB
Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/3.
 0 < < 1 : P is in e io o AB
To make he p og amming o he algo i hm mo e e icien ,
he gene al o mulas o he do p oduc o he ec o s and he
calcula ion o he dis ance be ween poin s a e con e ed
in o2D o m allowing use only basic ma hema ical ope a ions,
as shown by (5), (6) and (7).
√
(5)
(6)
(7)
Finally, a new a iable „s” will be in oduced, o indica e
he loca ion o R along he line con aining he sec ion PR.
( )
(8)
The sign o „s” indica es he side o he AB sec ion, whe e
poin R belongs o:
 s < 0: R is le o AB
 s > 0: R is igh o AB
 s = 0: R is on AB
A e inding he alue o „s” he dis ance o he pa h (PR)
and he dis ance o he sec ion endpoin (PB) can be calcula ed
as shown by (9) and (10).
(9)
(10)
Calcula ing he obo -sec ion dis ances can be done using
he algo i hm p esen ed abo e. Selec ing he sec ion wi h he
lowes dis ance alue is i ial, bu i is s ill no su e, ha he
selec ed sec ion will be he one o use as a s a sec ion. The
ini ial sec ion mus be wi hin a p ede ined dis ance om he
obo , and he sec ion’s o ien a ion mus be ma ching o he
obo ’s o ien a ion. Mo eo e , i he o ien a ion is ma ching,
he di ec ion mus be pe mi ed in he g aph, as well.
B. Di iding he nea es sec ion
A he poin whe e he pe pendicula posed om he obo
o he nea es sec ion has and in e sec ion wi h he sec ion line,
he sec ion is di ided in o wo pa s (Fig. 3, sec ions AP and
PB). The in e sec ion poin ’s dis ance o he sec ion endpoin s
will be calcula ed, and in he g aph sec ion AB will be
subs i u ed wi h sec ion AP and PB, inhe i ing me ada a, like
allowed di ec ions om he o me sec ion AB. The leng h o
he new sec ions will be calcula ed, oo.
C. Finding he sho es pa h
A g aph sea ching algo i hm can be used a his s age o
de e mine he sho es pa h o he goal s a ion. The widely
known A-s a algo i hm was selec ed o his pu pose, because
o i s ad an ageous ea u es in he aspec o pa h inding and
g aph a e sal, as p o ed in [12], [13].
V. CALCULATING THE ROBOT’S DISPLACEMENT
F om he Sick na iga ion lase senso he obo ’s posi ion
can be eques ed 3- imes a second, which is no enough
equen in o ma ion sou ce o con ol he obo ’s cen e
wi hin a desi ed dis ance om he p ede ined ou e a a
desi ed mo emen speed. To calcula e he ac ual posi ion da a
he obo ’s kinema ics needs o be de ined. Fig. 4 and Table
1a e in ended o illus a e and explain he kinema ics o a 2-
wheeled, di e en ial d i en obo .
Fig. 4. Kinema ics o a di e en ial d i e obo
TABLE 1.LEGEND FOR FIG. 4
No a ion
Explana ion
x, y
Robo 's Cu en posi ion
xg, yg
Goal posi ion
Θ
Robo 's cu en angle
Θg
Goal angle ela i e o obo 's angle
ωl, ω
Wheels' cu en angula speed
Wheel adius
Robo 's eloci y ec o
l
Robo - goal dis ance
The obo ’s ac ual posi ion and o ien a ion depending on
he wheels’ a e age angula speed since he las measu emen
poin , and he elapsed ime since he las measu emen can be
calcula ed using (11), (12) and (13).
Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/3.
󰇗
(11)
󰇗
(12)

󰇗
(13)
VI. CALCULATING THE CONTROLLER’S INPUTS
A wide ange o Fuzzy based con olling mechanisms o
di e en ial d i en mobile obo s has been published so a -
[14], [15], [16] and [17] we e used as basis o he con olle
design.
This con olle needs o be eed a leas wi h wo da a: goal
dis ance and goal angle -allowing he obo ollow he ou e
and d i e, slow down o s op whe e i is necessa y. The
calcula ion o he inpu s consis s o he ollowing s eps:
1. As he pa h- inding algo i hm e u ned he se ies o
coo dina es (i.e. he sec ion endpoin s) needed o
ouch by he obo , he coo dina es a e pushed in o a
FIFO s ack.
2. Ini ially he i s elemen is he nea es poin o he
obo .This poin will be aken ou o he s ack, and
made he i s empo a y goal, sogoal angle and goal
dis ance will be calcula ed o his poin .
3. The con olle is now eed wi h he calcula ed da a
un il he nex i e a ion.
4. I he obo is app oaching he empo a y goal, he
algo i hm pops ou a new coo dina e om he s ack,
and make i he new empo a y goal.
5. S ep 2 and S ep 4 a e epea ed un il he s ack ge s
emp y.
VII. DEFINITION OF THE FUZZY CONTROLLER
A. Membe ship unc ions
Fuzzy membe ship unc ions a e used o label anges o
da a in o o e lapping o non-o e lapping se s. This egula ion
uses wo inpu - and wo ou pu a iables:
Inpu 1 : Goal angle (Righ , Le )
Inpu 2 : Goal dis ance (Nea )
Ou pu 1 : A e age angula speed (S op, D i e)
Ou pu 2 : Angula speed di e ence (Gole , Go igh )
The ac ual de ini ions o he a iable’s membe ship
unc ion a eillus a ed on Fig. 5-8.Fig. 5-8 a e cap u ed om
he so wa e Q FuzzyLi e4 -a g aphical in e ace o he
uzzyli e open-sou ce Fuzzy Logic Con ol lib a y, w i en in
C++. Re e ence [18] has been used o e i ying he
unde lying design and ope a ion o he “ uzzyli e” lib a y.
Fig. 5. Membe ship unc ions o “Goal angle” inpu a iable
Fig. 6. Membe ship unc ion o “Goal dis ance” inpu a iable
Fig. 7. Membe ship unc ions o “A e age angula speed” ou pu a iable
Fig. 8. Membe ship unc ions o “Angula speed di e ence” ou pu
a iable
B. Fuzzy ule se
The six ules a e in ended o sol e he ollowing p oblems:
 Make he obo u n o he igh di ec ion, i he
„Goal angle” is „Righ ” o „Le ” (i.e. no ze o).
 Make he obo d i e, i he „Goal dis ance” is no
„Nea ”, and s op, when he dis ance is 100% „Nea ”.
 Make he obo dec ease i s speed, i i pe o ms
u ning mo emen .
The ules a e summa ized in Fig. 9.
Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/3.
1. IF GOALANGLEISLEFT
THEN ANGULARSPEEDDIFFERENCEISGOLEFT
2. IF GOALANGLEISRIGHT
THEN ANGULARSPEEDDIFFERENCEISGORIGHT
3. IF GOALDISTANCEISNEAR
THEN ANGULARSPEEDISSTOP
4. IF GOALDISTANCEISNOT NEAR
THEN AVGANGULARSPEEDISDRIVE
5. IF GOALANGLEISRIGHT AND GOALDISTANCEISNOT NEAR
THEN AVGANGULARSPEEDISSTOP
6. IF GOALANGLEISLEFT AND GOALDISTANCEISNOT NEAR
THEN AVGANGULARSPEEDISSTOP
Fig. 9. The Fuzzy ule se
VIII. CONCLUSION
This pape p esen ed a solu ion o d i ing 2-wheeled
di e en ial d i e mobile obo s on a so wa e designed pa h.
The indus ial g ade LIDAR senso ( h ough i s sa e y
ce i ica ions) makes he solu ion embeddable in o eal-wo ld
applica ions, like au oma ion o o kli s and o he indus ial
ucks. Fo es ing pu poses, an indi idual mobile obo was
also manu ac u ed. Running he so wa e implemen a ion o
he de ailed algo i hms on he es - obo is showing p omising
esul s, al hough plans a e a ailable o u he imp o emen s
o posi ioning accu acy and o suppo ing o he ypes o d i e
ains.
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www. uzzyli e.com/download/ uzzyli e-pape -3.1.pd