Recen Inno a ions in Mecha onics (RIiM) Vol. 2. (2015). No. 1-2.
DOI: 10.17667/ iim.2015.1-2/5.
1
Home Compa ible Omnidi ec ional Ho e c a
Robo
Ge gely Nagymá é
Dep . o Mecha onics Op ics and Enginee ing In o ma ics
Budapes Uni e si y o Technology and Economics
Budapes , Hunga y
nagyma e.ge gel[email p o ec ed]m
Zi a V. Fa kas
Dep . o Machine and P oduc Design
Budapes Uni e si y o Technology and Economics
Budapes , Hunga y
[email p o ec ed]me.hu
Abs ac —As obo s slowly in eg a e in o home en i onmen s,
syn hesis o na iga ion, maneu e abili y and human accep ance
is ine i able. This pape in oduces a holonomic ho e c a
design and he associa ed omnidi ec ional con olling algo i hm.
Ho e c a capabili ies we e in es iga ed and discussed hough
design ecommenda ions in ela ion o a obo compa ible
en i onmen . The main aim o he design was o achie e be e
maneu e abili y, enhanced capabili ies o o e coming obs acles,
and he elimina ion o he d i phenomena ha is a
cha ac e is ic o con en ional unde ac ua ed ho e c a designs,
whe e ea o o d i e exe s h us in one di ec ion. Due o own
ine ia and he low ic ion o he ai cushion, he ho e c a slips
ou in he o iginal di ec ion. Beyond sol ing his d i p oblem,
ano he key ea u e o ou design is he capabili y o be
con olled in a global e e ence ame ega dless o i s
o ien a ion and desi ed ajec o y wi h he help o a holonomic
h us e d i e. O ien a ion con ol is also implemen ed by
u ning he base o he h us e s. The design was implemen ed on
a emo e con olled ho e c a obo and p o ed o ha e a
supe io maneu e abili y o e con en ional ho e c a designs,
hus ou esea ch g ea ly con ibu es o u u e human- obo
coope a ion in he li ing en i onmen .
Keywo ds—ho e c a obo ; omnidi ec ional d i e; o ien a ion
con ol; obo compa ible en i onmen
I. INTRODUCTION
Rapid de elopmen o se ice obo s [1] is going o eme ge in
e e yday en i onmen s, whe e syn hesis o na iga ion,
maneu e abili y and human accep ance is managed unde
a ious condi ions, in o de o success ully execu e gi en
asks. Taking he obo 's capabili ies in o accoun and
synch onizing hem wi h he buil en i onmen , he obo
compa ible en i onmen is c ea ed [2], whe e mobile obo s
can na iga e and maneu e wi h high e iciency. Ope a ional
eliabili y and sa e y a e he basis o ho e c a obo s as
well, o in eg a e hem e icien ly in o he en i onmen , ha is
clu e ed wi h obs acles. Whe e de ec ing in o ma ion,
eaching o objec s, maneu e abili y, use iendly
communica ion a e basic necessi ies [3], ha moniza ion o
buil en i onmen in alignmen wi h digi al, physical and
in elligen space becomes emphasized [4][5]. This esea ch
in es iga es spa ial cha ac e is ics o su ounding en i onmen
in ela ion o ho e c a obo s and gi es ecommenda ions o
c ea e an en i onmen ha enhances na iga ion pa allel o isk
educ ion and haza d p e en ion [6][7]. In he nea u u e he
obo will be used by non enginee s o no obo specialis [8].
In he aspec o obo use s people can be di ided o 4 main
g oups[9].
- obo specialis enginee
- enginee , bu no obo specialis
- no enginee , bu being in e es ed in obo ics
- elde ly people, eluc an o obo ics
Fo obo s in ou daily li e i is no enough o execu e a p e-
p og ammed ac ion line. They mus be able o adop
hemsel es o changing en i onmen , make hei own decisions
and in addi ion, hey ha e o socially i in o he human
en i onmen . In he discussion design ecommenda ions o
ho e c a obo en i onmen compa ibili y a e in oduced.
This pape p esen s a unique ho e c a design and con ol
me hod designed o agile maneu e abili y in na ow places
be ween he a ge boxes. The obo is also con olled in he
global coo dina e sys em o he human ope a o , unlike
con en ional ho e c a , whe e he ajec o y and maneu e s
depend on he obo o ien a ion. Con en ional ho e c a
obo s a e unde ac ua ed and also su e om “d i ”. They
ha e ea o o d i e ha can exe h us in one di ec ion.
Du ing co ne ing, due o he own ine ia o he ho e c a and
he low ic ion o he ai cushion, he ho e c a will slip ou in
he o iginal di ec ion. The e a e con ol me hods ha imp o e
con ollabili y o hese ho e c a s o example wi h swi ching
Fuzzy con olle [10]. O he me hods aim o minimize sway
eloci y e o and heading e o [11].
The assigned ask is easie o pe o m wi h a holonomic
ho e c a . An omnidi ec ional design should be able o
elimina e d i and can be con olled in a global e e ence
ame ega dless o i s o ien a ion and desi ed ajec o y. An
au onomous ho e c a obo p esen ed by Roubieu and Se es
is based on a con en ional ho e c a design and uses wo
addi ional la e al h us e s o sideways mo emen s [12].
O ien a ion change is achie ed wi h he di e en ial d i e o he
wo ea h us e s. This solu ion does no ul ill ou
equi emen s. A obo p esen ed by De weile , G i in and
Roeh implemen s omnidi ec ional d i e wi h h ee h us e s
posi ioned in 120 deg ees gene a ing h us in a bi a y
Recen Inno a ions in Mecha onics (RIiM) Vol. 2. (2015). No. 1-2.
DOI: 10.17667/ iim.2015.1-2/5.
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di ec ions [13]. They use wo addi ional h us e s o o a ing
he obo . This solu ion sepa a es he omnidi ec ional d i e
om he o ien a ion con ol, howe e equi es ex a h us e s.
I hey a e used o o ien a ion egula ion, hen hey should
usually oscilla e a ound ze o e olu ion. This is a cos ly
solu ion and less e ec i e.Ou design is also ca ied ou wi h
h ee h us e s posi ioned in 120 deg ees o p ese e he
bene i s o omnidi ec ional d i ing. On he o he hand, he
o ien a ion egula ion is implemen ed by u ning he bases o
he h us e s. This solu ion spa es wo h us e s, bu equi es a
se o mo o and synch onous u ning o he bases.
The pape is dis ibu ed as ollows: Sec ion II desc ibes he
design and he pa s o he obo ; Sec ion III con ains a
discussion on he implemen ed o ien a ion egula ion; Sec ion
IV in oduces he omnidi ec ional con ol algo i hm; Sec ion V
discusses applica ion in obo compa ible en i onmen ; and
inally, conclusions a e d awn in Sec ion VI.
II. PARTS AND DESIGN
The base o he obo is an oc agonal ca bon ibe
composi e igid chassis. This is he base o he omnidi ec ional
d i es. The ai cushion o he ho e c a is p oduced by a
li ing p opelle and a lexible plas ic ski ha hangs down
om he chassis. The h us e s can be o a ed simul aneously
by a hidden oo hed bel unde he chassis d i en by an RC
se o mo o . The h us e s a e iPowe 2208/14 ype b ushless
DC (BLDC) mo o s wi h p opelle s. The mo o consoles and
p opelle sa e y g ids jus like many o he i ing on he obo
a e unique, 3D p in ed pa s. In he middle o he chassis he e
is he li ing mo o , which is he same ype BLDC wi h double
p opelle s o highe ai anspo a ion. Abo e he li ing mo o
he e a e he LiPo ba e y and he elec onics on a ca bon pipe
console, which lea es enough space o he ai inle o he
li ing mo o . The elec onics is based on a STM32F3
Disco e y boa d ha ca ies a STM32F303VCT6 ARM
Co ex-M4 MCU, LSM303DLHC 3 axis accele ome e -
magne ome e IC and a L3GD20 digi al ou pu gy oscope. A
3DoF obo ic a m is placed abo e he elec onics ha can ca y
and place he dices and is capable o emo ing dices o
opponen obo s. The a m is ac ua ed by high powe RC se os
and closed du ing obo na iga ion o achie e a cen alized
mass dis ibu ion, keeping he ai cushion o he ho e c a
homogenous. The design is shown in Fig. 1.
Omnidi ec ional d i ing equi es simila cha ac e is ic o
he h ee h us e s which a e desi ably linea . BLDC mo o s a e
pai ed wi h elec onic speed con olle s (ESC) and p opelle s
and a e cha ac e ized as one uni . The inpu alue is he PWM
du y cycle o he ESCs, whe eas he ou pu alue is he h us
gene a ed by he mo o -p opelle combina ions. The mo o s
we e a ached o a console such way ha hey exe h us
downwa ds. This ins alla ion was placed on a digi al scale o
measu e h us gene a ed by di e en du y cycles.
Fig. 2 shows he esul o he measu emen s. I can be seen
ha he cha ac e is ics a e no s ic ly linea bu linea enough
o ou con olle . Howe e , one o he h ee mo o s shows a
sligh ly mo e la cha ac e is ic ha was easily compensa ed
wi h a cons an mul iplica ion.
Fig. 1. Design plan and he manu ac u ed obo in ope a ion
Fig. 2. Th us e cha ac e is ics
Recen Inno a ions in Mecha onics (RIiM) Vol. 2. (2015). No. 1-2.
DOI: 10.17667/ iim.2015.1-2/5.
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III. MAINTAINING ORIENTATION
Pe pe ual knowledge o ehicle o ien a ion is essen ial in
he global ame con olling. The obo is equipped wi h
ine ial measu emen uni and compass senso , hus a comple e
Kalman based algo i hm o a simple g adien descen
o ien a ion es ima ion algo i hm could be used o calcula e
p ope h ee dimensional o ien a ions [14]. This ehicle mo es
in plane wi h h ee deg ees o eedom ied. The only possible
o a ion is he heading o a ion a ound he e ical axis. Pi ch
and oll angles na u ally ne e change, he e o e he e is no use
o he accele ome e eadings in he senso usion. The
compass senso could ha e se ed a g ea ole in measu ing
absolu e o ien a ion. Howe e , he magne ome e senso
p o ed o be useless on his small obo due o he expansi e
magne ic ield o he BLDC mo o s. The simple inal solu ion
uses only one da a om he gy oscope. I in eg a es he angula
eloci y a ound he e ical axis compensa ed wi h he o se
ou pu o he gy oscope. This o se is measu ed e e y ime he
ho e c a is se led. This simple solu ion p o ed o be
su p isingly eliable o se e al minu es o ope a ion. Since he
ho e c a is emo e con olled by a human, i is he ole o he
ope a o o send ±5° compensa ion ins uc ions o he obo
con olle , o compensa e long e m diso ien a ion.
The o ien a ion is inally main ained wi h a simple PID
con olle uned wi h he Ziegle - Nichols me hod [15]. The
ou pu o he con olle is he o que ha compensa es he
cons an o que o he li ing p opelle and keeps he obo in
he desi ed o ien a ion, which is basically he ini ial o ien a ion.
IV. OMNIDIRECTIONAL CONTROL ALGORITHM
The con ol algo i hm is sepa a ed o calcula ion o basic
o ces, hei o a ion and compensa ion o yield desi ed o que.
A. Calcula ing Basic Fo ces o Omnidi ec ional D i e
The x-y e e ence o ces a e gi en by he ope a o as
desi ed di ec ion and accele a ion in he global coo dina e
sys em. In ce ain cases he obo o ien a ion is changed by he
ope a o . The e o e, he e e ence o ces a e ans o med in o
he ho e c a coo dina e sys em wi h he ollowing equa ions:
𝐹𝑥=𝐹𝑥𝑟𝑒𝑓 ∙cos(−𝛾)−𝐹𝑦𝑟𝑒𝑓 ∙sin(−𝛾)
𝐹𝑦=𝐹𝑦𝑟𝑒𝑓 ∙cos(−𝛾) + 𝐹𝑥𝑟𝑒𝑓 ∙sin(−𝛾)
whe eFxand Fy a e he desi ed o ces in he obo coo dina e
sys em, Fx e and Fy e a e in he global coo dina e sys em and γ is
he obo o ien a ion angle ela i e o he global y axis. E e y
u he calcula ion is also in e p e ed in he obo e e ence
ame.
The x-y o ces hen ans o med o pola coo dina es wi h
equa ion 3 and 4. 𝛽=𝑎𝑟𝑐𝑡𝑔𝐹𝑦
𝐹𝑥
𝐹𝑎𝑏𝑠 = 𝐹𝑥2+𝐹𝑦2
Rela ion be ween obo coo dina e sys em and wo ld
coo dina e sys em is shown in Fig. 3.
Fig. 3. Robo coo dina e sys em in ela ion o wo ld coo dina e sys em
The lines o ac ion o he h us s in e sec in he obo ’s
cen e poin wi h enclosed angles o 120 deg ees. The
p opelle s exe h us only in one di ec ion. Fabs could be
basically decomposed on o he wo adjacen lines o ac ion.
Howe e , he e will always be a minimal h us exe ed on he
hi d line o ac ion. This is due o he conside a ion ha none o
he mo o s is sho down comple ely any o he mo o s du ing
ope a ion. BLDC mo o s ake some ime o un up co ec ly.
Wi h an inpu signal aking hem o a minimal easible speed, a
smoo he con ol can be achie ed. This minimum speed exe s
6% o he maximum h us ha wo ks agains he wo e ec i e
o ces. The C code snippe ha is used o decompose Fabs o he
basic o ces aking he minimal e e se h us in o accoun is
shown below.
i ((be a>-0.5236)&&(be a<1.57)){
F2=0.06;
F3=(F2*cos(0.5236)+Fx)/cos(0.5236);
F1= F3*sin(0.5236)+Fy+sin(0.5236)*F2;
}
else
i ((be a<-2.61799)||(be a>1.57)){
F3=0.06;
F2=-(-F3*cos(0.5236)+Fx)/cos(0.5236);
F1= F3*sin(0.5236)+Fy+sin(0.5236)*F2;
}
else
i ((be a>-2.61799)||(be a<-0.5236)){
F1=0.06;
F3=(F1+ an(0.5236)*Fx-
Fy)/(2*sin(0.5236));
F2= (F3*cos(0.5236)-Fx)/cos(0.5236);
}
Resul o he decomposi ion is shown in Fig. 4, in wo
example pic u es aken om a LabVIEW simula ion.
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Recen Inno a ions in Mecha onics (RIiM) Vol. 2. (2015). No. 1-2.
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Fig. 4. Fxand Fy e e ence o ces in he obo coo dina e sys em a e decomposed o he h ee lines o ac ion o he d i ing mo o s
B. Compensa e Th us wi h Requi ed To que
The o ien a ion egula o calcula es he equi ed o que o
keep obo o ien a ion s eady. This o que is ob ained by
u ning he lines o ac ion o h us gene a ing mo o s, so ha
hey do no c oss he obo ’s cen e o mass. Fo ce componen s
(F 1, F 2, F 3) appea pe pendicula o he basic o ces de ined
by he omnidi ec ional d i e (Fa1, Fa2, Fa3). Fig. 5 shows he
desc ibed o ces, whe e M is he desi ed o que, α is he o a ed
angle o he mo o s in he algo i hm, Fm1, Fm2, Fm3 a e he
o ces inally applied by he mo o s and is he dis ance o he
mo o s’ o a y bases om he cen e .
Fig. 5. Fo ce ec o s and equi ed o que
The equi ed o que is he sum o he applied o ques by
angen ial o ces:
𝑀=𝐹𝑟1∙𝑟+ 𝐹𝑟2∙𝑟+ 𝐹𝑟3∙𝑟
These o ces can be exp essed wi h he o a ion angle and
he known adial o ces equi ed o he omnidi ec ional d i e:
𝑀=𝐹𝑎1∙ an ∝∙𝑟+ 𝐹𝑎2∙ an ∝∙𝑟
+ 𝐹𝑎3∙ an ∝∙𝑟
Ro a ion angle can be exp essed om he abo e equa ion:
∝=𝑎𝑟𝑐𝑡𝑔 𝑀
𝐹𝑎1+𝐹𝑎2+𝐹𝑎3 ∙𝑟
Knowing he o a ion, applied o ces by he mo o s can be
calcula ed as ollows:
𝐹𝑚1= 𝐹𝑎1
cos ∝
𝐹𝑚2=𝐹𝑎2
cos ∝
𝐹𝑚3=𝐹𝑎3
cos ∝
P io hese calcula ions a condi ional addi ion is applied. I
he sum o he basic o ces does no each a speci ied minimum
hen balanced o ces a e added o hem, so α o a ions la ge
han 40 deg ees will no be equi ed. This is necessa y due o
mechanical limi a ions and o each smoo he o ien a ion
con ol. The men ioned minimum o ce depends on he applied
equi ed o que.
V. DISCUSSION
The p oposed ho e c a is a sui able applica ion in he
obo compa ible en i onmen . Ho e c a obo s compa ed o
wheeled obo s s and ou in hei capabili y o slide o e he ai
cushion. S ee ing in case o con en ional ho e c a obo s is
di e en om holonomic ho e c a o wheeled d i e, and
di ec d i es used as mobile obo pla o ms. In case o
con en ional ho e c a s ee ing mo o is coupled wi h a
h us e so as o h us ai along he axis o h us e suppo ed
by udde blades (pe pendicula o he axis o h us e ). As
udde h us ai is de lec ed o le o igh , s ee ing he obo
la e ally, d i ing is a nega i e aspec . In case o a holonomic
ho e c a d i p oblem is o e come by using 3 h us e s
posi ioned in 120 deg ees wo k oge he wi hou he need o
udde blades, hus su icien maneu e abili y is achie ed.
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Ho e c a can mo e o e une en su ace and ini ial
ac ion is no needed compa ed o wheeled obo s. S ill
haza dous maneu e s can be p oblema ic, hus in case o
mo emen o e a amp, low s eepness is necessa y o he
obo o a oid ins abili y o losing ack. Longe amps need
p ope edge p o ec ion, meanwhile should no be ob usi e o
human use . Ramp design equi es ex a space be o e and a e
he amp, i shall be designed o lea e u ning diame e and
mo o o que o oll on o and o he amp sa ely.Floo su ace
wi h openings in case o wheeled obo s leads o s uck wheels,
while in he case o ho e c a ,ai cushion leakage ha leads o
mo emen s op. When a ca pe has oo high piles o a su ace
is oo bumpy i can also lead o s op o haza dous maneu e ing.
I is impo an o examine he obo and i s en i onmen o
damage conce ns ega ding impac esis ance, en apmen
a oidance and heigh di e ences.
To achie e na iga ional asks, knowledge o obo
dimensions is necessa y: wid h, leng h, heigh , u ning
diame e , si ua ion o manipula o a ms, weigh , possible speed
and mo o o que. Tu ning space and maneu e ing space
should be adequa e. TDH u ning diame e o a holonomic obo
is he minimum u ning diame e , i is he same as obo ’s
o e all diame e and u ning midpoin esides a he cen e
poin o he obo , whe e X is he maximum wid h and Yis he
maximum leng h o he obo :
𝑇𝐷𝐻= 𝑋2+𝑌2
TDDIR u ning diame e o a di ec d i e obo is he
minimum u ning diame e , which is app oxima ely wice he
size o he maximum diame e o he obo . Whe e X is he
wid h and Y is he leng h o he obo , D is he dis ance
be ween he inne ixed and on s ee ed wheel and δ is he
maximum s ee ing angle:
𝑇𝐷𝐷𝐼𝑅 = 2 × 𝑋+𝐷
an 𝛿 2
+𝑌2
Fig. 6. Tu ning diame e and maneu e ing o holonomic and di ec d i es
Maneu e ing equi es u n in e e se di ec ion in a na ow
space in case o di ec d i e, as shown in Fig. 6. While
omnidi ec ional mo emen in 3 DoF enables no only senso s
o ac ua o s, bu he whole body o he obo o ha e di e en
o ien a ion om he ac ual mo ing di ec ion.
Tu ning wi h a holonomic ho e c a obo is achie ed by
simul aneous h us ec o ing and an i- o que con ol. The e is
p essu ized ai cushion unde nea h he chassis, when loaded i
needs o be balanced cen ally, no o le ai escape om unde
he ski . S opping o he obo is c ea ed wi h calib a ed
h us e s, and dec easing li p opelle speed, hus holonomic
ho e c a can s op e icien ly.
In an indoo en i onmen p oblems o ho e c a obo s a e
noise and ai dis u bance. The e is he noise o he mo o s bu
noise le el o igina ing om h us e s is qui e high, ac o s like
diame e o blades and blade ip o m a e aking pa in noise
gene a ion. Wi h bigge diame e o blades g ea e o ce can be
achie ed wi h slowe p opelle speed, hus less ib a ion and
noise. Wi h he e olu ion o p opelle s, unique h us e blade
su ace and edge design wi h enclosed unnel like casing will
be possible, ha c ea es less u bulence, quie p opelling and
g ea e a io o di ec ed ai , which can lead o mo e p ecise
maneu e ing. In he u u e, when obo and human sha e li ing
space in he home, sound le els a e an impo an conside a ion,
quie e ai low will mee a be e accep ance. Mo o s
encapsula ed wi hin obo case can lowe noise le el. S ill, in
an en i onmen , whe e indoo o ou doo a ea co e s g ea
dis ances and noise is no a ac o ho e c a obo s a e al eady
ad an ageous.
While mos obo s a e es ic ed indoo s, ho e c a obo s
a e able o explo e ou doo en i onmen s wi h une en su ace
cha ac e is ics. In many ins i u ions, like hospi als, communal
homes, mul i-building pa ks, om leng hy co ido s o in
be ween buildings a eas, hey can be used o anspo e o
cou ie pu poses (e en wi h human guidance), ha would be
di icul o signi ican ly slowe o a wheeled obo . Mo eo e
ho e c a needs ewe esou ces o he same dis ance, due o
i s speed and weigh , ene gy usage is lowe , ha ansla es in
lowe CO2 emission.
To c oss heigh gaps o p e en ipping, adequa e g adual
amps a e needed o obo s. Many amps ha e been buil due
o accessible buil en i onmen egula ions. The e is no need
o u he cons uc ion wo ks o dis u bance o he buil
acili ies.
While wheeled obo s ha a e p one o ge s uck in be ween
chai legs, a holonomic obo can manage o con inue i s
mo emen by dynamically adjus ing h us e angles when
app oaching an obs acle. Holonomic ho e c a obo can
change i s o ien a ion du ing mo emen , hus mo e na u al and
lexible d i ing is possible. In an en i onmen whe e u ni u e
o obs acles a e p esen (~2cm doo sills, chai legs, ca pe s,
co ds o cable co e s on he g ound) obo s ill needs o be
capable o seamless maneu e s as shown in Fig. 7 and Fig. 8.
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Fig. 7. Holonomic ho e c a obo c ossing o e co d
Fig. 8. Holonomic ho e c a obo c ossing o e a 2cm high doo sill
In ega d o he ski design o he ho e c a 's ski less
u bulen , smoo h ai low is c ea ed wi h ci cula shape
es ic ing he ou wa d expansion o ski . Ou e su ace o ski
needs enhanced du abili y and semi- igid s uc u e ha educes
ic ion and wea ou du ing c ossing o e obs acles o
app oaching/lea ing amps, while keeping elas ici y ha helps
mo emen con inui y and p e en s damage o objec o inju y
o human. P opelle s o o he o a ing pa s need sa e y gua d,
while no limi ing ai low.
In ega d o main enance, wheeled obo s collec dus
a ound hei wheel bea ings and spinning pa s, o can ge
s uck in ca pe pile, ho e c a obo is less p one o his e ec .
Ne e heless, pe iodic audi s and e iews o obo and i s
en i onmen mus be ensu ed o de e mine main enance o sa e
and isk ee ope a ion.
VI. CONCLUSION
The omnidi ec ional ho e c a design and con ol
algo i hm desc ibed in his pape opens new pe spec i es in
design o ho e c a ype obo s. This design o e s supe io
maneu e abili y in na ow places and also simple
con ollabili y by au oma ion o emo e con olling. Use s
equi e se ice asks om obo , hus obo needs balanced
obo compa ible en i onmen o be complian wi h hose
equi emen s. Du ing he p ocess o in eg a ing obo s in o he
e e yday en i onmen , ha combines na iga ion, adap abili y
and accessibili y, ho e c a obo s g ea ly con ibu e o u u e
use and in eg a ion o sa e, eliable and e ec i e human- obo
coope a ion.
ACKNOWLEDGMENT
We hank o he inancial suppo gi en by Ligh wa e L d.,
MOGI Depa men o Budapes Uni . o Technology and
Economics and he Mecha onical Depa men o S uden
College o Mechanical Enginee ing. Au ho s g a e ully
app ecia e he “MaMSTAR” eam o mecha onics enginee ing
s uden s o he common wo k on he obo .
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