Uni e sidade do Minho
Escola de Engenha ia
An ónio João Gonçal es Ma os
Mo ion planning o obo ic a ms in eg a ed on
mobile pla o ms o in e nal logis ics asks
Janua y 2025
Uni e sidade do Minho
Escola de Engenha ia
An ónio João Gonçal es Ma os
Mo ion planning o obo ic a ms in eg a ed on
mobile pla o ms o in e nal logis ics asks
Mas e ’s Disse a ion
Mas e ’s in Mechanical Enginee ing
Specializa ion in Mecha onic Sys ems
Wo k de eloped unde he supe ision o :
P o esso José Mendes Machado
P o esso Luís Filipe Cas o F ei as Lou o
Janua y 2025
i
DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR
TERCEIROS
Es e é um abalho académico que pode se u ilizado po e cei os desde que espei adas as
eg as e boas p á icas in e nacionalmen e acei es, no que conce ne aos di ei os de au o e
di ei os conexos.
Assim, o p esen e abalho pode se u ilizado nos e mos p e is os na licença abaixo indicada.
Caso o u ilizado necessi e de pe missão pa a pode aze um uso do abalho em condições
não p e is as no licenciamen o indicado, de e á con ac a o au o , a a és do Reposi ó iUM
da Uni e sidade do Minho.
Licença concedida aos u ilizado es des e abalho
A ibuição
CC BY
h ps://c ea i ecommons.o g/licenses/by/4.0/
ii
Acknowledgmen s
Fi s ly, I would like o exp ess my deepes g a i ude o my supe iso José Machado, o
his suppo h oughou he de elopmen o his wo k and o P o esso Luís Lou o o his
in aluable guidance in all ma e s ela ing o obo ics.
I wan o exp ess my hea el hanks o P o esso Es ela Bicho o he gene osi y in
sha ing knowledge and o he willingness o help me whene e I needed i .
A special acknowledgmen goes o he eam in ol ed in his p ojec , namely P o esso
Sé gio Mon ei o and my colleagues I an Cas o, João Ve íssimo, João Diogo, and João A aújo,
wi h special a en ion o he la e o pu ing me h ough his delica e phase.
I am also hank ul o he Bosch eam o hei collabo a ion wi h he Uni e si y o Minho,
wi h special ecogni ion o Tiago Ca alho and Damásio Eu ico o hei dedica ion du ing ou
egula mee ings o moni o he p ojec ’s p og ess.
I am g a e ul o he en i e Ma Lab eam a he Indus ial Elec onics Depa men o
wa mly welcoming me du ing hese pas mon hs and o p o iding he ools and esou ces
needed o accomplish his wo k.
I also wan o exp ess my g a i ude o Paulo Bou bon om Eu opneumaq o allowing me
o conduc es s wi h he g ippe used in his p ojec .
I app ecia e my amily, whose unwa e ing suppo has been my ock du ing his
challenging pe iod. Thei encou agemen was undamen al.
Thank you o he Depa men o Mechanical Enginee ing p o esso s o he knowledge
impa ed du ing my academic jou ney o e he pas i e yea s.
Las ly, I wan o hank my iends who sha ed his challenging jou ney wi h me. Special
hanks o he Roubocopo g oup.
iii
STATEMENT OF INTEGRITY
I he eby decla e ha ing conduc ed his academic wo k wi h in eg i y. I con i m ha I ha e no
used plagia ism o any o m o undue use o in o ma ion o alsi ica ion o esul s along he
p ocess leading o i s elabo a ion.
I u he decla e ha I ha e ully acknowledged he Code o E hical Conduc o he Uni e si y
o Minho.
i
Abs ac
The de eloped wo k in his disse a ion is pa o he MIAR p ojec , which ocuses on using
synch onized Mobile In elligen Au onomous Robo s (MIAR) o au oma e logis ics ope a ions
a Bosch Ca Mul imedia B gP. The au onomous mobile manipula o mus pe o m pick-and-
place ope a ions in ol ing Ta ge s, boxes con aining ce ain elec onic p oduc s, be ween a
s o age bu e and access amps connec ed o he assembly lines. The pu pose o his
disse a ion was o de elop mo ion planning o he KUKA LBR iiwa 14 R820 manipula o o
execu e he in ended asks. The use o a edundan a m in his p ojec aimed o c ea e
collision- ee ajec o ies in con ined spaces. Fi s ly, a simula ion model was c ea ed a
CoppeliaSim o ep esen he Bosch shop loo whe e he mobile manipula o will ope a e.
Unde his scena io, se e al asks we e pe o med, such as de e mining he numbe o boxes
he manipula o could handle om he dollies and checking he maximum numbe o boxes
ha could be anspo ed on op o he mobile pla o m. To ca y ou he planning es s, he
collabo a i e g ippe 2FGP20 was selec ed o mee he p ojec ’s equi emen s, and cus om-
designed inge s we e simula ed a Au odesk Fusion o wi hs and he imposed loads du ing
manipula ion. Addi ionally, new op imized amps we e in oduced o ensu e ha he a m
could access boxes.
A me hod o communica ion be ween CoppeliaSim and Mo eI , so wa e used o
ajec o y gene a ion, was implemen ed. This communica ion was es ablished using ROS2 ia
wo launch iles. A benchma king s udy was conduc ed among en planne s, iden i ying T-RRT
as he mos sui able o he p ojec . Subsequen ly, he planne was cus omized o ensu e
be e esul s ac oss di e se manipula ion scena ios, and a pos -p ocesso was u ilized o
e i y i i would lead o signi ican imp o emen s, conside ing he p ojec 's s ingen
equi emen s.
In conclusion, he manipula o demons a ed sa is ac o y pe o mance, gi en he
complexi y o i s wo king en i onmen . Some limi a ions we e iden i ied, and sugges ions o
u u e imp o emen s we e p oposed.
Keywo ds: Global Planne s, Mo ion Planning, Pick-and-Place, Smoo hness.
Resumo
O abalho desen ol ido nes a disse ação enquad a-se no p oje o MIAR, que se oca na
u ilização de Robôs Au ónomos In eligen es Mó eis (MIAR) sinc onizados pa a au oma iza as
ope ações de logís ica na Bosch Ca Mul imedia B gP. O manipulado mó el au ónomo
necessi a de ealiza ope ações de pick-and-place en ol endo Ta ge s, caixas con endo
de e minados p odu os ele ónicos, en e um bu e de a mazenamen o e ampas de acesso
ligadas às linhas de mon agem. O obje i o des a disse ação oi desen ol e planeamen os de
mo imen o pa a o manipulado KUKA LBR iiwa 14 R820 pode execu a as a e as p e endidas.
A u ilização de um b aço edundan e nes e p oje o oi com a in enção de se c ia aje ó ias
li es de colisões em espaços con inados. P imei amen e, oi c iado um modelo de simulação
no CoppeliaSim pa a ep esen a o chão de áb ica na Bosch, no qual o manipulado mó el i á
ope a . Nes e cená io, o am ealizadas di e sas a e as, ais como de e mina a quan idade
de caixas que o manipulado pode ia alcança dos dollies e e i ica a quan idade máxima de
caixas que pode iam se anspo adas em cima da pla a o ma mó el. Pa a a ealização dos
es es de planeamen o, oi selecionado o g ippe colabo a i o 2FGP20, de o ma a sa is aze
os equisi os do p oje o, e o am simulados den es pe sonalizados no Au odesk Fusion pa a
supo a as ca gas impos as du an e a manipulação. Além disso, o am in oduzidas no as
ampas o imizadas pa a ga an i que as caixas pudessem se acedidas pelo b aço.
Foi desen ol ido um mé odo de comunicação en e o CoppeliaSim e o Mo eI ,
so wa e que é u ilizado pa a a ge ação de aje ó ias. Es a comunicação oi es abelecida po
ROS2 a a és de dois launch iles. Um es udo de benchma king en e dez planeado es oi
ealizado, iden i icando o T-RRT como o mais adequado pa a o p oje o. Pos e io men e, o
planeado oi pe sonalizado de o ma a ga an i melho es esul ados em di e sos cená ios de
manipulação, e um pós-p ocessado oi adicionado pa a e i ica a exis ência de melho ias
signi ica i as, pe an e os igo osos equisi os do p oje o.
Concluiu-se que o manipulado demons ou um desempenho sa is a ó io pe an e a
complexidade do ambien e de abalho do p oje o. Fo am ainda iden i icadas algumas
limi ações e p opos as suges ões de melho ias u u as.
Pala as-cha e: Pick-and-Place, Planeado es Globais, Planeamen o de Mo imen os,
Sua idade.
i
Con en s
Abs ac ..................................................................................................................................... i
Resumo .......................................................................................................................................
1 In oduc ion ........................................................................................................................ 1
1.1 Mo i a ion ................................................................................................................... 2
1.2 Objec i es .................................................................................................................... 3
1.3 S uc u e o he Disse a ion ....................................................................................... 4
2 S a e o he A ................................................................................................................... 6
2.1 The Impo ance o Collabo a i e Robo s in Indus y .................................................. 6
2.2 Au oma ic Sys ems o Feeding and Collec ing Boxes om P oduc ion Lines ........... 9
2.3 Mo ion Planne s ........................................................................................................ 14
2.3.1 Global Planne s .................................................................................................. 15
2.3.2 Local Planne s ..................................................................................................... 24
2.4 Mo ion Planning and Con ol o Au onomous Mobile Manipula o s ...................... 28
3 Theo e ical Founda ions and De elopmen Tools ........................................................... 31
3.1 Fundamen al Concep s o Mo ion Planning .............................................................. 31
3.2 Mo ion Planne s U ilized in he MIAR P ojec .......................................................... 33
3.2.1 PRM* .................................................................................................................. 34
3.2.2 LazyPRM* ........................................................................................................... 35
3.2.3 KPIECE ................................................................................................................. 35
3.2.4 T-RRT .................................................................................................................. 36
3.2.5 Bi-TRRT ............................................................................................................... 37
3.2.6 BiEST ................................................................................................................... 38
3.2.7 P ojEST ................................................................................................................ 39
3.3 Ha dwa e Componen s ............................................................................................. 39
ii
3.3.1 Fo wa d Kinema ics ............................................................................................ 40
3.3.2 In e se Kinema ics ............................................................................................. 49
3.4 So wa e Tools ........................................................................................................... 53
3.4.1 ROS2 Middlewa e ............................................................................................... 53
3.4.2 Mo eI Lib a y .................................................................................................... 59
3.4.3 CoppeliaSim ........................................................................................................ 64
3.4.4 Au odesk Fusion ................................................................................................. 66
4 De eloped Wo k ............................................................................................................... 67
4.1 Sys em A chi ec u e .................................................................................................. 67
4.2 Simula ion Model ...................................................................................................... 68
4.3 Selec ion o he G ippe ............................................................................................ 73
4.4 De elopmen o he G ippe Finge s ......................................................................... 78
4.4.1 Modeling he G ippe Finge s ............................................................................ 79
4.4.2 E alua ion and simula ion o he inge s ........................................................... 80
4.4.3 Finge s Tes ........................................................................................................ 84
4.5 Maximum Numbe o Ta ge s o be Manipula ed .................................................... 86
4.6 Con igu a ion in Mo eI ............................................................................................ 90
4.6.1 Launch KUKA LBR iiwa 14 R820 + 2FGP20 in R iz .............................................. 92
4.6.2 Mo eI -CoppeliaSim Communica ion ................................................................ 94
4.7 Ramp Analysis and Op imiza ion ............................................................................... 97
4.8 Pick-and-Place Ope a ions in Mo eI /CoppeliaSim ................................................ 102
5 Analysis o Resul s .......................................................................................................... 109
5.1 Selec ion o he Ideal Mo ion Planne ..................................................................... 109
5.2 Analysis o he Mo ion Planne s Compa ison ......................................................... 112
5.3 Op imiza ion o he Mo ion Planne ....................................................................... 116
5.4 Manipula ion Ope a ions Using he Selec ed Mo ion Planne ............................... 118
xi
Lis o Tables
Table 1 - Mo ion ange and speed speci ica ions o he KUKA LBR iiwa 14 R820 join s. ........ 40
Table 2 - Dena i -Ha enbe g pa ame e s able o he KUKA LBR iiwa 14 R820 obo . ........ 42
Table 3 - Func ional and non- unc ional equi emen s o MIAR p ojec g ippe . ................. 75
Table 4 - Compa ison o p oduc a ibu es. ............................................................................ 76
Table 5 - Topics and messages used o he Mo eI -CoppeliaSim communica ion. ............... 96
x
Lis o Ac onyms
Ac onym
Desc ip ion
AMR
Au onomous Mobile Robo
AS/RS
Au oma ed S o age and Re ie al Sys em
B gP
B aga Plan
BP
Bounce Pos u e
CAD
Compu e -Aided Design
CAE
Compu e -Aided Enginee ing
CHOMP
Co a ian Hamil onian Op imiza ion o Mo ion Planning
D-H
Dena i -Ha enbe g
DMP
Dynamic Mo emen P imi i e
DoF
Deg ees o F eedom
EST
Expansi e Space T ees
FK
Fo wa d Kinema ics
GC
Global Con igu a ion
GTP
Good- o-Pe son
HRC
Human-Robo Collabo a ion
HUMP
Human-like Uppe -limb Mo ion Planne
IK
In e se Kinema ics
KMR
Kuka Mobile Robo
KPIECE
Kinodynamic Planning by In e io -Ex e io Cell Explo a ion
LiDAR
Ligh De ec ion and Ranging
MIAR
Mobile In elligen Au onomous Robo s
OMPL
Open Mo ion Planning Lib a y
PRM
P obabilis ic Roadmap Me hod
ROS
Robo Ope a ing Sys em
RRT
Rapidly Explo ing Random T ee
RULA
Rapid Uppe Limb Assessmen
SEW
Shoulde -Elbow-W is
SEW
Vi ual Shoulde -Elbow-W is
x i
SKU
S ock-Keeping Uni
SP
S a pos u e
SRDF
Seman ic Robo Desc ip ion Fo ma
S-R-S
Sphe ical-Ro a ional-Sphe ical
STOMP
S ochas ic T ajec o y Op imiza ion o Mo ion Planning
TAP
Ta ge Am Pose
TEB
Time Elas ic Band
TP
Ta ge Pos u e
T-RRT
T ansi ion-based Rapidly Explo ing Random T ee
URDF
Uni ied Robo Desc ip ion Fo ma
XML
Ex ensible Ma kup Language
YAML
Ye Ano he Ma kup Language
1
1 In oduc ion
A Bosch Ca Mul imedia B aga Plan (B gP), as well as in o he ac o ies wi hin he g oup, he
mo emen o boxes con aining elec onic p oduc s, known as Ta ge s, ac oss he shop loo
be ween a ious assembly lines is a complex ask. Cu en ly, Ta ge s a e mo ed manually, a
ime-consuming p ocess ha o en esul s in missed deli e y deadlines. This issue has se e al
implica ions o ope a ional pe o mance and p oduc ion cos s.
The p esen disse a ion is pa o he “Connec ed Manu ac u ing - Digi al
T ans o ma ion” P og am ( e : SIFN-01-9999-FN-179826 – I&D) o he Bosch & UMinho
pa ne ship, mo e speci ically he P ojec CM.5G.P16 – MIAR – “Flexible sys em o anspo
p oduc s be ween sha ed p ocesses wi h Mobile In elligen Au onomous Robo s (MIAR)
synch onized wi h p oduc ion lines”. The MIAR p ojec aims o de elop in elligen , lexible,
and au oma ed solu ions ha enable he anspo and posi ioning o p oduc s wi hin
es ablished deadlines, elying on a combina ion o ad anced echnologies and solu ions in
a eas such as collabo a i e obo ics, au oma ion, compu e ision, and IoT.
Wi hin he scope o he MIAR p ojec , i is necessa y o add ess he p e iously
men ioned si ua ion by implemen ing inno a i e echnologies. The goal is o mo e he Ta ge s
om manual o au oma ed h ough solu ions ha gua an ee as e p ocedu es, espec ing
p ede ined ime ames. The solu ions o be implemen ed aim o use synch onized
au onomous mobile manipula o obo s in eg a ed wi h p oduc ion lines o pe o m pick,
anspo , and place ope a ions o he Ta ge s. Fo his pu pose, ision sys ems a e equi ed
o iden i y he Ta ge s and po en ial obs acles o he mo emen o he au onomous mobile
obo , such as humans, since he en i onmen in which he obo will ope a e is sha ed wi h
ac o y wo ke s. Fu he mo e, since he in en ion is o use mo e han one au onomous mobile
manipula o obo in he es ablished ope a ions, i is impo an o ensu e ha no collisions
occu be ween hem du ing he execu ion o asks. To achie e his, i is necessa y o de elop
a lexible lee managemen sys em designed o he espec i e obo s. I is also essen ial o
con ol he mo emen o he edundan an h opomo phic obo ic a m moun ed on he
mobile pla o m o ensu e he success ul execu ion o pick, anspo , and place asks.
2
In he con ex o my disse a ion, he goal is o de elop and es me hods o gene a ing
collision- ee pick-and-place mo emen s o he obo ic a m in eg a ed in o he mobile obo .
The obo ic a m is esponsible o picking he Ta ge s om he s o age bu e and placing
hem on o he access amps leading o he assembly lines. I mus also collec emp y boxes
om he amps and e u n hem o he s o age bu e . As hese obo s mus coexis wi h
human ope a o s, in addi ion o sa e y, an impo an equi emen is ha hei mo emen s
a e legible o make he obo 's beha io mo e anspa en o he wo ke s a ound hem.
1.1 Mo i a ion
Due o he cons an echnological e olu ion in Indus y 4.0, he use o au oma ed sys ems o
con ol indus ial p ocesses has g own. The main pu pose is o maximize he p oduc i i y and
lexibili y o he p ocesses by in eg a ing au onomous machines in mono onous and
haza dous ope a ions and educing human in e en ion (NECULA e al., 2022). Cu en ly, asks
such as anspo ing and handling componen s ac oss p oduc ion lines emain challenging in
manu ac u ing en i onmen s. The inc easing demand o adap able wo kspaces equi ing
mo e lexible asks has inc eased he need o collabo a i e obo s in he indus y. The use o
collabo a i e obo s in sha ed en i onmen s wi h humans enables hem o assis wo ke s in
a ious asks, pa icula ly epe i i e ones (Weidemann e al., 2023).
The MIAR p ojec is conce ned wi h implemen ing a p omising app oach o ensu e he
p ecise and sa e placemen and collec ion o boxes in he p oduc ion lines. This is achie ed by
in eg a ing an omnidi ec ional mobile pla o m equipped wi h a edundan collabo a i e
manipula o . This sys em is designed o wo k wi h human wo ke s in a sha ed indus ial space.
As such, he obo ic a m's mo emen s mus be sa e and human- eadable du ing all he pick-
and-place ope a ions.
Mo eo e , he obo ic a m's en i onmen is expec ed o be illed wi h access amps ha
a e p esen ed as obs acles o he manipula o ’s mo emen s. The obo mus gene a e
collision- ee ajec o ies o p ecisely deli e he boxes o he designa ed amps wi hou
colliding wi h hem du ing he en i e p ocess. Consequen ly, he s udy o he edundancy o
he manipula o wi h he mobile pla o m’s posi ion will b ing good bene i s o he execu ion
o he in ended ope a ions. The p oposed goal b ings he oppo uni y o ealize an in-dep h
3
analysis o he a ailable mo ion planning echniques o c ea e a smoo h and e icien
ajec o y h oughou all ope a ional phases.
1.2 Objec i es
The main objec i e o his disse a ion is o de elop me hods and algo i hms o gene a ing
sa e and p ecise mo emen s o he obo ic a m, ensu ing he accu a e and secu e placemen
o boxes on o he eeding lines, as well as he simula ion wi h he manipula o o alida e he
de eloped models.
The planning o ajec o ies o he edundan a m consis s o execu ing a ious
manipula ion asks. These asks in ol e picking up and placing Ta ge s be ween he s o age
bu e and he au onomous mobile obo (AMR) and, in u n, picking up and placing hese
boxes on o he access amps. To ul ill his p ima y goal, a se ies o p elimina y asks mus be
unde aken, such as amilia izing wi h he Robo Ope a ing Sys em (ROS) and Mo eI
amewo ks. The c ea ion o a simula ion scena io eplica ing he eal en i onmen a Bosch
Ca Mul imedia B gP using he physical simula o CoppeliaSim as well as de e mining he
numbe o boxes he AMR can anspo ac oss he shop loo a e undamen al o box
manipula ion managemen .
Ano he impo an sub ask o conside is he s udy o possible modi ica ions in he “as
is” sho loo , pa icula ly he access amps, which in he cu en scena io e eal di icul ies
o he placemen o he Ta ge s. Alongside hese sugges ed changes, his esea ch will also
ex end o he sea ch o an app op ia e g ippe in he ma ke o he obo ic a m. The g ippe
mus be capable o g asping he boxes o manipula ion while sa is ying he p ojec 's
equi emen s.
To ensu e he obo ic a m's mo emen s a e legible and sa e, a comp ehensi e
o e haul o he collision- ee ajec o y planne s will be conduc ed. A compa a i e analysis o
hese planne s will be made o selec he mos p ope one o he pick-and-place ope a ions.
This disse a ion also aims o se le a means o communica ion be ween Mo eI , he
mo ion planne lib a y esponsible o p ojec ing he obo ’s mo emen s, and he physical
simula o CoppeliaSim, which will ansmi all he physical in e ac ions and o e all ope a ions.
As expec ed ou comes, he goal is o achie e a obo ic a m capable o pe o ming sa e
and human- eadable mo emen s du ing pick-and-place ope a ions o boxes in he p oduc ion
4
a ea. This is pa icula ly impo an as he obo will coexis in an en i onmen wi h human
ope a o s, whe e human- obo in e ac ion mus be as e icien as possible.
1.3 S uc u e o he Disse a ion
This disse a ion is di ided in o six chap e s, each explained below. The cu en chap e
se es as he in oduc ion, add essing he p oblem de ini ion, p o iding con ex o he MIAR
p ojec , and ou lining he mo i a ions and goals es ablished o his wo k.
The second chap e exposes he cu en g ow h in he use o obo s in he indus y,
ocusing on he e olu ion o collabo a i e obo s in sha ed asks. I also includes a gene al
e iew o collision- ee mo ion planne s, especially sampled-based, op imiza ion-based, and
human-like planne s. I add esses an analysis o he indus y's exis ing au oma ic eeding and
collec ion sys ems o boxes, and i exhibi s an o e iew o solu ions simila o he obo ic
app oach p esen ed in he MIAR p ojec , emphasizing con ol by mo ion planning o mobile
pla o ms and in eg a ed obo ic a ms.
The hi d chap e explo es heo e ical ounda ions impo an o p ope ly
unde s anding he de eloped wo k and del es in o he impac o edundancy in he obo ic
a m's kinema ics s udy. I also lays ou he planne s unde examina ion in he p ojec o he
pick-and-place ajec o ies. Las ly, i de ails all he so wa e and ha dwa e necessa y o ealize
he espec i e wo k.
The ou h chap e ep esen s he co e o his disse a ion. I desc ibes he sys em
a chi ec u e o he MIAR p ojec and de ails all he p ac ical asks ca ied ou du ing he
p ojec , commencing wi h he c ea ion o he simula ion scena io in CoppeliaSim, he s udy
o he numbe o boxes he AMR can disloca e, and he selec ion o an app op ia e g ippe o
he manipula ion asks. I includes he modeling and simula ion o po en ial g ippe inge s o
be used in he p ojec . The design o op imal access amps o acili a e pick-and-place
ope a ions o he Ta ge s is also examined. O he asks we e also execu ed, such as
con igu ing he manipula o wi h he g ippe in Mo eI , eplica ing he obo ’s wo kspace
en i onmen o he R iz, and es ablishing communica ion be ween Mo eI and CoppeliaSim.
The i h chap e ho oughly compa es he mo ion planne s in oduced in Chap e 3 o
iden i y he mos sui able one o he p ojec . Consequen ly, i includes he esul s and
5
analysis o he benchma king s udy. I also explo es cus omized planne s and examines how
hei adjus men s in luence he pe o mance o he pick-and-place ope a ions.
The inal chap e p o ides a comp ehensi e summa y o he wo k accomplished
h oughou his esea ch, highligh ing he conclusions d awn om he de eloped solu ion. I
discusses he possible limi a ions o he p oposed app oach and ou lines sugges ions o
u u e esea ch.
The disse a ion concludes wi h an annex and appendices ha include echnical
d awings o he access amps, he inge s designed o he selec ed g ippe , and he esul s o
he mo ion planne s compa ison.
6
2 S a e o he A
This chap e begins by discussing he e olu ion o collabo a i e obo s in he indus y and
p o ides a li e a u e e iew on au oma ed solu ions o he collec ion and placemen o boxes
on p oduc ion lines. I also summa izes mo ion planning me hodologies ha ensu e collision-
ee mo emen , ca ego izing hem in o global and local planne s. Finally, he chap e
highligh s some applica ions o hese me hodologies in mobile manipula o obo s.
2.1 The Impo ance o Collabo a i e Robo s in Indus y
Indus y 4.0 ep esen s a majo ans o ma ion in indus ial p ocesses. This digi al
indus y elies on cybe -physical sys ems and he In e ne o Things o connec da abases
be ween sys ems and equipmen , such as senso s and p ocesso s, o p omo e a sa e and
mo e e icien indus y (Tok aş-Palu , 2022).
In mode n indus y, obo s a e he as es -expanded mechanical solu ion implemen ed
in he indus ial sec o (S. Liu & Liu, 2020). Based on he Wo ld Robo ics 2023 epo , he
wo ldwide annual ins alla ion o indus ial obo s has ipled om 2012 o 2022, p esen ing a
sligh inc ease o 5% om 2021 o 2022. This g ow h can be checked in Figu e 1 – (a) g aph.
Besides, be ween 2021 and 2022, he e was a no able inc ease in he annual Ins alla ions o
Indus ial obo s by cus ome indus y, mainly in he elec ical/elec onics sec o o 10% and
in he au omo i e sec o o 16%, as depic ed in Figu e 1 – (b).
Figu e 1 - (a) Annual ins alla ions o Indus ial obo s - Wo ld; (b) Annual Ins alla ions o Indus ial obo s by cus ome
indus y – Wo ld. Adap ed om (IFR In e na ional Fede a ion o Robo ics, 2023).
7
Companies adop mo e and mo e indus ial obo s o hei ex ensi e usabili y in
ope a ional p ocesses such as manu ac u ing and logis ics, especially obo ic a ms, o execu e
epe i i e, exhaus ing, and dange ous asks like a c and spo welding, ca ying high loads,
sol ing manual labo p oblems, and ensu ing highe p oduc ion e iciency. These ypes o
obo s a e usually in a obo ic cell equipped wi h senso s and p o ec i e ences o su ound
he obo ’s wo kspace o ensu e he sa e y o human wo ke s (Weidemann e al., 2023).
Indus ial obo s ha e been de ined in di e en ways o e he yea s. The Robo
Ins i u e o Ame ica (1979) s a es ha an indus ial obo is “a ep og ammable,
mul i unc ional manipula o designed o componen s o specialized de ices, h ough
p og ammed mo ions o he pe o mance o a a ie y o asks” (Considine & Considine,
1986). Acco ding o he in e na ional s anda d EN ISO 10218-1:2011 (In e na ional
O ganiza ion o S anda diza ion, 2011a), which speci ies sa e y equi emen s o indus ial
obo s, an indus ial obo is “an au oma ically con olled, ep og ammable, mul ipu pose
manipula o , p og ammable in h ee o mo e axes, which can be ei he ixed in place o mobile
o use in indus ial au oma ion applica ions.”
Despi e he con inued g ow h o adi ional obo s, he e is an inc easing demand o
mo e dynamic wo k en i onmen s whe e asks a e less s uc u ed, and wo ke s can
collabo a e alongside obo s (Palmie i & Scoccia, 2021). In hese cases, he obo s don’ ha e
p o ec i e ences and wo k aided by sa e y senso s and image p ocessing h ough came as.
Consequen ly, he s udy and de elopmen o collabo a i e obo s ha e expanded.
Collabo a i e obo s, also known as cobo s, eme ged in he 1990s. A collabo a i e
obo is de ined as a obo designed o di ec in e ac ion wi h a human wi hin a de ined
collabo a i e wo kspace (ISO 10218-2:2011 (In e na ional O ganiza ion o S anda diza ion,
2011b)).
In con as o adi ional obo s, he pu pose o cobo s is o wo k alongside humans in
a a ie y o indus ial applica ions like palle izing, machine ending, assembly, and injec ion
molding, as well as in o he a eas such as heal hca e and assis ance o people in need. Cobo s
ha e been s eadily e ol ing o e he yea s o make collabo a ion wi h humans mo e e icien
and sa e and o enable imp o emen s in wo kplace e gonomics. They will p ima ily be used
o epe i i e asks ha equi e high p ecision and load-li ing capabili ies (Weidemann e al.,
2023).
14
2.3 Mo ion Planne s
Robo ic a ms a e pa icula ly sui ed o p ocesses ha in ol e picking and placing
componen s, whe e iming and p ecision a e c i ical. Fo a obo ic a m o success ully
anspo boxes, as equi ed o he MIAR P ojec , i is essen ial o plan i s mo emen s
ca e ully o a oid collisions wi h obs acles in he wo king a ea and wi h he obo i sel . As
manipula o s a e inc easingly equi ed o challenging ope a ions, o en wo king in igh
spaces and collabo a ing wi h humans, he impo ance o e ec i e mo ion planning con inues
o g ow. Mo ion planning has been a subjec ho oughly explo ed o yea s (LaValle, 2006),
which consis s o de e mining a obo 's mo ion om an ini ial s a e o a a ge s a e, a oiding
en i onmen al obs acles, and sa is ying cons ain s, such as join and o que limi s (La ombe,
1991). The mo ion planning algo i hms can be ca ego ized in o:
• Classical (De e minis ic/Combina o ial) Me hods: These me hods de ine an explici
ep esen a ion o he opology o he con igu a ion space. They a e igo ous in
disc e izing he con igu a ion space and sea ching o he bes pa h, o en leading o
highe compu a ional demands as he dimensionali y o he con igu a ion space
inc eases. The combina o ial me hods a e decomposed by he cell decomposi ion,
po en ial ields, and oadmap app oaches (Chose e al., 2005).
• G id Me hods: These app oaches disc e ize he con igu a ion space in o a g id
s uc u e, acili a ing sea ches o iable pa hs (Ma ia & Rod igues, 2022).
• Sampling-Based Me hods: These echniques u ilize de e minis ic o andom sampling
o explo e he con igu a ion space, making hem pa icula ly adep a handling high-
dimensional p oblems.
• Op imiza ion-Based Me hods: These me hods aim o gene a e op imal ajec o ies
based on speci ic c i e ia, such as minimizing pa h leng h, mo o e o s, o
compu a ion ime. Op imiza ion-based me hods can p oduce e icien and smoo h
pa hs bu migh equi e signi ican compu a ional powe .
• Human-Like Mo ion Planning Me hods: Wi h he inc easing in eg a ion o obo s in o
sha ed wo kspaces alongside humans, mo e and mo e mo ion planning algo i hms
p io i ize legibili y and p edic abili y. These me hods aim o gene a e in ui i e
mo emen s o humans, enhancing sa e y and collabo a ion (Gulle a e al., 2021).
15
Howe e , mo ion planning algo i hms a e ypically classi ied in o wo ypes o pa h-planning
me hods o obs acle a oidance: he global and local me hods (Hwang & Ahuja, 1992). The
ollowing sec ions will discuss he concep o each me hod and p o ide an o e iew o some
exis ing mo ion planning algo i hms o each.
2.3.1 Global Planne s
The global mo ion algo i hms (Hwang & Ahuja, 1992) consis o me hods ha p ocess
in o ma ion abou he obo ’s wo kspace be o e execu ing he mo emen . These me hods a e
used when he mo ion planning mus be me iculously planned. The p ocess in his planne is
made o line. An example is planning mo ion ajec o ies o indus ial obo s in en i onmen s
whe e a oiding obs acles is c ucial. In he global app oach, since he wo kspace is s a ic, he
mo ion planning o obo ic a ms becomes easie , esul ing in gene a ed mo emen s ha a e
mo e ai h ul o human mo emen s and p o iding mo e p edic able ac ions o he human
ope a o s a ound he obo ’s wo kspace. Some mo ion planning algo i hms classi ied as global
me hods, such as sampling-based planne s and op imiza ion-based Planne s, a e p esen ed
below.
2.3.1.1 Sampling-based Planne s
Sampling-based mo ion planning has been one o he mos esea ched pa h-planning
me hods in ecen yea s. These me hods a e widely adop ed in high-dimensional spaces (Hsu
e al., 1997). The sample-based me hods also e e ed o as p obabilis ic me hods, use andom
o de e minis ic sampling unc ions o explo e he con igu a ion space (C-space). The main
pu pose o hese planne s is o sol e pa h-planning p oblems by cons uc ing g aphs o ees
h ough he connec ion o sampled con igu a ions (Chose e al., 2005). The e o e, hese
planne s can be di ided in o wo main phases: he i s phase in ol es sampling he
con igu a ion space o c ea e a oadmap, and he second is sea ching his oadmap o ind an
op imal pa h (Ba land, 2012). Among all ypes o planne s, he mos popula a e he
P obabilis ic Roadmap (PRM) and he Rapidly Explo ing Random T ee (RRT) (Elbanhawi &
Simic, 2014).
2.3.1.1.1 P obabilis ic Roadmap Me hod
The P obabilis ic Roadmap Me hod (PRM), in oduced by Ka aki e al. (1996), is a
planning me hod ha sea ches o ee collision pa hs o obo ic manipula o s wi h many
deg ees o eedom (DoF), known o e ec i ely sol ing complex mo ion planning p oblems.
16
This me hod in ol es c ea ing a oadmap (a g aph) in he con igu a ion space and sea ching
o he op imal pa h. The eby, he algo i hm comp ises wo dis inc phases: he lea ning
phase and he que y phase. In he lea ning phase, he algo i hm cons uc s a p obabilis ic
oadmap by con inuously gene a ing nume ous andom con igu a ions wi hin he obo ’s
Collision- ee space (C ee). These collision- ee con igu a ions a e ep esen ed as nodes in a
g aph, and due o a local planne , ee collision pa hs a e calcula ed by binding he nea by
con igu a ions (nodes) oge he , gene a ing he edges o he oadmap. The que y phase
consis s o inding he mos easible pa h be ween a speci ied ini ial con igu a ion (qini ) and
a inal con igu a ion (qgoal) on he oadmap c ea ed in he lea ning phase. The me hod
a emp s o ind he nodes on he oadmap closes o he nodes ep esen ing he ini ial and
inal con igu a ions and hen es ablishes a connec ion be ween hose nodes. Subsequen ly, a
pa h- inding algo i hm is pe o med o ind he sho es pa h be ween he con igu a ions. An
ad an age o he PRM algo i hm is he abili y o handle many ypes o obo s wi h a bi a y
DoF, and i doesn’ equi e de ailed in o ma ion abou he obo ’s con igu a ion space. I only
equi es he abili y o e i y whe he a gi en con igu a ion is collision- ee. Figu e 8 shows an
example o he cons uc ion o a oadmap.
Figu e 8 - Example o building a oadmap on a obo . Obs acles a e ep esen ed in blue. Adap ed om (E ic O. Sco , 2015).
The e ha e been se e al ex ensions o he PRM planne o e he yea s, such as he
Lazy PRM algo i hm de eloped by Bohlin & Ka aki (2000) In his me hod, he collision
checking is only ca ied ou a e a pa h be ween he ini ial and inal con igu a ions is ound,
signi ican ly educing compu a ional ime in many scena ios. To do his, his app oach ini ially
conside s ha all he oadmap nodes and edges a e collision- ee be o e sea ching o he
sho es pa h, and only a e wa d a e he nodes and edges checked o collisions.
17
2.3.1.1.2 Rapidly Explo ing Random T ee
The Rapidly Explo ing Random T ee (RRT) de eloped by LaValle (1998) was designed
o sol e mo ion planning p oblems wi h algeb aic and di e en ial cons ain s in high-
dimensional spaces. This p obabilis ic me hod c ea es a g aph in he shape o a ee ha is
expanded apidly wi hin he obo ’s con igu a ion space. To implemen his me hod, de ining
he en i onmen , he ini ial and goal poin s, and he maximum numbe o samples is
necessa y. The ee is oo ed om he ini ial s a e and g ows inc emen ally by selec ing and
connec ing andom poin s un il i ei he eaches he goal posi ion, he numbe o i e a ions,
o he planning ime expi es (Kang e al., 2019). A new poin , co esponding o a new obo
s a e, is andomly gene a ed o each i e a ion. The nea es poin o he ee is sea ched, and
a local planne a emp s o ex end he ee o he sampled poin . I he new poin is collision-
ee, i is added o he ee, c ea ing a new b anch. When he algo i hm is unable o ind a
solu ion in some ins ances, he p oblem can be add essed by execu ing he algo i hm wi h
mo e samples. Unlike he PRM, which equi es he cons uc ion o a oadmap and he
connec ion o nea by con igu a ions, in he RRT, he samples a e ob ained uni o mly, causing
he ee o g ow in o egions o he collision- ee space ha ha e no ye been explo ed. As a
esul , RRT is widely used in high-dimensional spaces and nonholonomic and kinema ic mo ion
planning asks (Gaspa e o & Zano o, 2010). The RRT planne is o en as e han he PRM
planne because i ocuses on inding he nea es neighbo poin o each i e a ion. A he
same ime, he PRM sea ches h ough mul iple neighbo poin s a ound a andom sample.
Figu e 9 illus a es an example o he cons uc ion o a con igu a ion ee.
Figu e 9 - Example o he building o an RRT ee. Adap ed om (Ba land, 2012).
2.3.1.1.3 RRT-Connec
The RRT-Connec algo i hm, de eloped by La alle & Ku ne (2000), also known as
bidi ec ional RRT, was designed o e icien single-que y pa h planning. This app oach apidly
18
inds solu ions by explo ing he con igu a ion space wi h wo andom ees ha g ow owa d
each o he wi h a simple heu is ic. The algo i hm s a s by c ea ing wo ees: one “ o wa d”
ee oo ed in he ini ial obo con igu a ion and he o he “backwa d” ha s a s a he goal
con igu a ion. In his single-que y p obabilis ic planne (B. Scia icco & O iolo, 2009) he ees
expand inc emen ally by selec ing a sample o he C ee. One o he ees hen eaches ou
owa d he sample, c ea ing a new con igu a ion. The algo i hm a emp s o connec he
con igu a ion o he nea es e ex o he o he ee h ough a “Connec ” unc ion ha
i e a i ely ies o link he wo ees. I an obs acle is ound in he connec ion, he ees swi ch
oles, and he algo i hm s a s he nex i e a ion. RRT-Connec is conside ed p obabilis ically
comple e, which means ha he p obabili y o inding a solu ion inc eases wi h longe
planning ime. I is also usually as e han he s anda d RRT, especially in less clu e ed
en i onmen s, mainly because i ocuses on connec ing he wo ees, while RRT explo es wi h
a single ee un il i eaches he goal s a e.
2.3.1.1.4 RRT*
The Rapidly Explo ing Random T ee S a (RRT*) algo i hm de eloped by Ka aman &
F azzoli (2011) is a a ia ion o he single- ee RRT algo i hm designed o ensu e easible and
op imal pa hs acco ding o a speci ied cos unc ion. RRT* add esses he asymp o ic
op imali y, which means ha as numbe o samples inc eases, he p obabili y o inding he
op imal pa h app oaches one. This algo i hm modi ies he RRT by in oducing a p ocess ha
con inuously ewi es he sea ch ee. Fo each i e a ion, he algo i hm s a s by conside ing
ha he minimal cos connec ion will come om he closes sample o he ee. The e o e, a
new sample poin is added o he ee, and he connec ions o nea by con igu a ions a e e-
e alua ed o ensu e ha hey con ibu e o he mos cos -e ec i e pa h. This i e a i e p ocess
is con inuously op imized un il an op imal pa h is ound. Al hough he RRT* p o ides
signi ican ly be e solu ions, i equi es inc eased compu a ional cos since he p ocess o
ewi ing he ee demands addi ional calcula ions, leading o longe compu a ional imes and
a slowe con e gence a e. Ne e heless, adding asymp o ic op imali y in his sampling-based
me hod inc eases he ime complexi y by only a cons an ac o o e he s anda d RRT and
s ill p o ides be e pa hs.
2.3.1.2 Op imiza ion-based Planne s
Op imiza ion-based planne s add ess mo ion planning asks as op imiza ion p oblems,
whe e he goal is o compu e he mos e icien ajec o y ha sa is ies a se o cons ain s
19
ela ed o he obo . To ind an op imal ajec o y, an objec unc ion mus be de ined, wi h
he use selec ing wha pa ame e s wan s o op imize, such as ime, ene gy, o o he ac o s
(Ba land, 2012). These planne s o en use ei he g adien -based me hods, which op imize by
inc emen ally adjus ing he ajec o y, o non-g adien me hods, which explo e a b oade
ange o possible solu ions (Lynch & Pa k, 2017). Al hough hese me hods a e widely used due
o hei capaci y o gene a e ajec o ies ha op imize cos , hese app oaches don’ always
ensu e an e ec i e solu ion. Among he se e al ajec o y op imiza ion app oaches, some
echniques s and ou .
2.3.1.2.1 Co a ian Hamil onian Op imiza ion o Mo ion Planning
Zucke e al. (2013) in oduced an op imiza ion-based mo ion planne named
Co a ian Hamil onian Op imiza ion o Mo ion Planning (CHOMP) algo i hm ha uses
co a ian g adien and unc ional g adien echniques o op imize obo ajec o ies o
smoo hness and obs acle a oidance. This app oach is based on he po en ial ield wo k o
Quinlan & Kha ib (1993). Unlike mos mo ion planne s ha ea planning and op imiza ion as
sepa a e s ages in ajec o y gene a ion, CHOMP me ges hese phases h ough g adien -
based op imiza ion echniques o c ea e an en i ely op imizing ajec o y. CHOMP models a
ajec o y as a sp ing-mass sys em, whe e he pa h in e nal ene gy is ela ed o he leng h and
smoo hness, and he ex e nal ene gy is ela ed o he obs acles. This algo i hm seeks o
iden i y he mos e icien pa h ha minimizes he o al ene gy o he ajec o y. The
ajec o y's cos is de ined by wo componen s: he smoo hness unc ional o he planne ,
which measu es he dynamics quan i ies o he ajec o y, which aims o educe quan i ies
like he squa ed eloci y no m du ing he execu ion ime, and he obs acle-a oidance
unc ional ha implemen s cos unc ions in he obo ’s ope a ional space o keep he
algo i hm complexi y low (Gulle a e al., 2021). The planne quickly adjus s he ajec o y o
a oid collisions while op imizing dynamic quan i ies like he obo 's join eloci ies and
accele a ions.
2.3.1.2.2 S ochas ic T ajec o y Op imiza ion o Mo ion Planning
Ano he op imiza ion-based mo ion planne , known as S ochas ic T ajec o y
Op imiza ion o Mo ion Planning (STOMP), was de eloped by Kalak ishnan e al. (2011). This
algo i hm was designed o obo ic a ms o gene a e smoo hness ajec o ies ha a oid
obs acles and minimize cos s ela ed o cons ain s in a gi en ime. Unlike g adien
op imiza ion me hods like CHOMP, STOMP doesn´ equi e g adien s o he planning. As
20
men ioned, i op imizes gene al cos s like o que limi s, ene gy, and cons ain s included in
cos unc ions. This planne s a s by andomly gene a ing, a each i e a ion, a se o noisy
ajec o ies a ound an in easible ini ial ajec o y h ough a no mal p obabili y dis ibu ion.
These noisy ajec o ies a e e alua ed based on a cos unc ion ha includes e ms like
ajec o y smoo hness and obs acle a oidance. The esul s om he e alua ion a e used o
i e a i ely upda e o a ajec o y wi h lowe cos . The highe -cos ajec o ies con ibu e less
o he inal op imized pa h. I is conside ed ha bo h ini ial and inal a m pos u es in he
ajec o y a e pe manen du ing he op imizing p ocess, and he du a ion o a gi en ajec o y
is ixed. STOMP bene i s om i s abili y o quickly compu e dis ance que ies and collision cos s
using dis ance ields and sphe ical app oxima ions. Since STOMP is no a g adien -based
app oach, i has he ad an age o o e coming local minima issues, a common p oblem in
CHOMP. Fu he mo e, p ac ical expe imen s e ealed ha STOMP p esen s a be e success
a e in a ious manipula ion ope a ions han CHOMP.
2.3.1.3 Human-like Planne s
The e is an inc easing in e es in ensu ing ha obo s collabo a e wi h humans on
sha ed asks. Human-Robo In e ac ion/Collabo a ion (HRI-C) is enhanced when obo s
possess an an h opomo phic appea ance and exhibi mo emen s simila o hose o humans.
This makes hei ac ions less unp edic able and aids human pe cep ion in unde s anding
obo ic beha io . In o he wo ds, humans can in ui i ely ollow a obo 's mo emen s and
an icipa e i s u u e ac ions (Gulle a e al., 2020). E en hough p obabilis ic-based
app oaches ha e been ex ensi ely explo ed and s udied o e he pas decade, hese planne s
usually p oduce unp edic able ajec o ies (Ra ael & Fe ei a, 2022). Uns able mo emen s,
such as sudden ope a ing speeds by obo s, can cause anxie y among nea by humans and
pose dange s in sha ed en i onmen s (Zacha ias e al., 2011). Human-like mo phology and
mo emen a e key cha ac e is ics o e ec i e human- obo in e ac ions. Robo ic mo emen s
should be pe cei ed as na u al, p edic able, and capable o demons a ing he unde lying
in en o he ac ion wi hou he need o e bal communica ion (Gulle a e al., 2021).
The e o e, he s udy o legible and smoo h obo ic mo emen s has led o he de elopmen o
a ious human-like app oaches inspi ed by he human mo o p inciples p esen ed below.
2.3.1.3.1 RULA C i e ion wi h RRT-Connec
Zacha ias e al. (2011) de eloped a global me hod o edundan obo s using he RULA
(Rapid Uppe Limb Assessmen ) e gonomic esea ch c i e ion o gene a e human-like
21
mo emen s. In his me hod, he c i e ion is applied o iden i y he a eas in he wo kspace o
a manipula o whe e i exhibi s con igu a ions simila o hose o a human. RULA measu es
s ess and s ain le els in human uppe limb pos u es on a 1 o 7 scale. The lowe he RULA
sco e, he mo e na u al he obo con igu a ion is (McA amney & Co le , 1993). The ini ial
and desi ed con igu a ions o he a m a e de e mined h ough in e se kinema ics guided by
RULA. Subsequen ly, he ajec o y o mo e he a m be ween he wo con igu a ions is
gene a ed using he RRT-Connec sampling algo i hm, he eby de ining a collision- ee
ajec o y. To ind he na u al con igu a ions, he obo ’s dex e ous wo kspace is composed
o egions wi h a eachabili y index o measu ing he success in inding in e se kinema ics
solu ions. The ea e , he RULA c i e ion is applied o his map, whe e poin s wi h high RULA
sco es a e excluded, indica ing less na u al pos u es. A d awback o his me hod is ha i we
se a lowe RULA sco e equi emen o planning, we will ha e ewe alid manipula o
con igu a ions, esul ing in ewe in e se kinema ics solu ions. Addi ionally, his me hod also
o e looks he ypical empo al pa ame e iza ion seen in human mo emen s, leading o an
un ealis ic planning ime o he obo .
2.3.1.3.2 Bi-RRT Algo i hm wi h TAPs
Xie e al. (2011) in oduced he TAP “Ta ge Am Pose” concep o planning human-like
a m mo emen s in obo ic manipula o s. Be o e s a ing a ask, humans p ojec hei a m's
inal pose, called TAP. TAPs a e de ined h ough a quali a i e assessmen using pe o mance
indices ha compa e he obo ic a m's con igu a ion wi h he human a m's pose in speci ic
a ge posi ions. In a collision- ee pa h, a minimum je k model is employed o gene a e
smoo h mo emen s. To apply he model, he ini ial pos u e o he obo ic a m, he s a poin ,
he endpoin , and a se o waypoin s mus be known. Nex , he minimum je k model c ea es
a pa h o he inge h ough all hese poin s. TAPs a e calcula ed a each waypoin and a ge
posi ion o ensu e he obo 's mo emen pa e ns mimic human a ms. The IK-JJL in e se
kinema ics algo i hm enables he end-e ec o o ollow he inge pa h while eaching he
designa ed TAPs. In a scena io wi h obs acles, a global space analysis iden i ies high- isk
collision a eas. C ucial poin s a e selec ed o c ea e TAPs o he a m ha a oid hose
obs acles. The a m's pa h is segmen ed, and he Bi-RRT algo i hm is applied o each segmen
o de e mine a collision- ee pa h. A disad an age o his solu ion is he lack o conside a ion
o ypical human mo ion eloci y p o iles, such as he bell-shaped eloci y p o ile (Gulle a e
al., 2021).
22
2.3.1.3.3 Analy ical In e se Kinema ics Sol e o An h opomo phic 7-DOF Redundan
Manipula o s wi h Human-Like Con igu a ion Cons ain s
W. Liu e al. (2017) p oposed an analy ical in e se kinema ics algo i hm o se en
deg ees o eedom obo manipula o s wi h shoulde -elbow-w is (SEW) con igu a ion. This
algo i hm is designed o eplica e human con igu a ions om eco ded human mo emen s. I
in oduced he concep o key posi ions, which a e ca esian posi ions o he join s o he
manipula o . A co espondence me hod named w is -elbow-in-line allows mapping key
posi ions om human demons a ions o he manipula o . The men ioned key posi ions
co espond o he shoulde , elbow, w is , and end-e ec o /hand (Figu e 10 – (a)). Only he
key posi ions o he manipula o 's elbow and w is join s a e used as cons ain s o de ine he
obo a m con igu a ion since he key posi ion o he shoulde is known because i ’s ixed, and
he ask de e mines he end-e ec o . In his me hod, he key posi ion o he w is mus be
aligned wi h he manipula o 's elbow and end-e ec o key posi ions, ensu ing all emain
wi hin he same e e ence plane. Addi ionally, he key posi ion o he manipula o 's elbow
mus be as close as possible o he human elbow's key posi ion (Figu e 10 – (b)). When
mapping he key posi ions om he human demons a ion o he obo , he obo 's join limi s
and link leng hs mus be conside ed. The e o e, his solu ion allows he obo ’s elbow key
posi ion o be he closes o he human’s elbow key posi ion by adjus ing i e a i ely he
obo ’s w is key posi ion un il a alid analy ical in e se kinema ics solu ion is ound. A
disad an age o his solu ion lies p ecisely in sol ing he co espondence p oblem. As a
s a egy o i e a ing key posi ions is applied, he obo 's con igu a ion ceases o ollow a
human-like pos u e in a eas nea he join limi s o he obo ic a m.
Figu e 10 - (a) Kinema ic s uc u e o a obo and human a m and hei espec i e key posi ions; (b) Co espondence
me hod w is -elbow-in-line. Adap ed om (W. Liu e al., 2017).
23
2.3.1.3.4 Human-like Uppe -limb Mo ion Planne
Gulle a e al. (2021) p oposed a mo ion planning algo i hm named HUMP - Human-
like Uppe -limb Mo ion Planne . This planne was implemen ed o poin - o-poin mo emen s
and pick-and-place ope a ions, does no equi e a high compu a ional cos , and con empla es
biological empo al pa ame e iza ion h ough Fi s' Law. In his global me hod, ajec o ies
a e p e-planned o line o a oid collisions du ing he obo ’s pa h be o e s a ing i s
mo emen s h ough senso y inpu in o ma ion om he wo kspace. To p o ide a smoo h and
human-like mo ion, he a ge pos u e (TP), which co esponds o he obo con igu a ion ha
places he obo ’s end-e ec o in he in ended pose, mus be chosen o minimize he angula
je k o he mo emen be ween he obo ’s s a pos u e (SP) and he TP. This mo emen in
join s-space is e e ed o as di ec mo emen (Figu e 11 – (a)). I obs acles a e an icipa ed in
he di ec mo emen , bounce Pos u es (BP) a e selec ed o acili a e a back-and- o h
mo emen , which in ol es mo ing om SP o BP and back o SP. In his way, his algo i hm
conside s he di ec mo emen and back-and- o h mo emen , which a e used on pa hs wi h
obs acles. When hese wo mo emen s a e combined, a collision- ee ajec o y is de ined
(Figu e 11 – (b)). In he p oposed me hod, he mo emen was composed o pick, place, and
mo e segmen s (Figu e 11 – (c)). The pick and place mo emen s combine h ee phases:
anspo , app oach, and e ea . The app oach phase co esponds o he momen when he
manipula o mo es close o g asp he objec in he pick segmen and when he objec is
placed in he desi ed posi ion in he place segmen . Meanwhile, he e ea phase co esponds
o he momen when he objec is li ed in he pick segmen and when he manipula o mo es
away om he placemen posi ion in he place segmen . The mo e segmen includes he
anspo phase, which mo es he g ippe owa d he desi ed posi ions. The app oach and
e ea phases a e linked by he ac ions o g asping and ung asping he manipula ed objec .
All hese phases equi e he selec ion o a TP and he gene a ion o di ec mo emen . The
anspo phase is he only one ha in ol es bounce pos u es o gene a e back-and- o h
mo emen s and subsequen ly c ea e a composi e mo emen , as i is he only phase ha
conside s objec s along he pa h.
30
Ras ega panah e al. (2021) p oposed a gene ic amewo k designed o au oma e he
p ocess o emo ing and so ing componen s om elec ic ehicle ba e ies wi h he help o
mobile manipula o s. The amewo k enables mobile manipula o s o pick up componen s
om a able and place hem in he co ec bins. The amewo k comp ises na iga ion, whe e
he obo mo es a ound he wo ks a ion, conside ing he objec s in he en i onmen o each
he in ended loca ions. The na iga ion is handled h ough a global and local planne app oach.
The global me hod uses lase scan senso s ha ec ea e he wo kspace in a 2D g id map, and
he mobile base planning is sol ed by he A* algo i hm. The RRT planne plans he
manipula o 's ajec o y wi h an in e se kinema ics sol e o gene a e a collision- ee pa h.
The g ippe 's g asping ac ions a e con olled ia ROS.
31
3 Theo e ical Founda ions and De elopmen Tools
This chap e p o ides he necessa y heo e ical backg ound o suppo he concep s applied
in his disse a ion. Fi s ly, i aims o cla i y some basic concep s o mo ion planning ha a e
essen ial o he p ojec ’s de elopmen . While he p e ious chap e p o ided an o e iew o
mo ion planning and included examples o a ious planne s, Sec ion 3.2 highligh s he
impo ance o selec ing an app op ia e mo ion planne o manipula ion asks and de ails he
planne s deployed in he MIAR p ojec . This chap e also in oduces he manipula o used in
he MIAR p ojec , o e ing a comp ehensi e examina ion o i s kinema ics p ope ies h ough
he discussion o bo h o wa d and in e se kinema ics. A las , his chap e o e s a
comp ehensi e o e iew o he so wa e and amewo ks u ilized in he con ex o his
disse a ion.
3.1 Fundamen al Concep s o Mo ion Planning
Wi hin he scope o mo ion planning, i is impo an o di e en ia e wo concep s: pa h
planning and ajec o y planning. Pa h planning is a componen o he b oade mo ion
planning p oblem aimed a de e mining a collision- ee pa h be ween wo con igu a ions in
he wo ld space wi hou conce n o dynamics, he du a ion o mo ion, o o he cons ain s
(Lynch & Pa k, 2017). On he o he hand, T ajec o y planning no only deals wi h geome ic
(kinema ical) p oblems bu also wi h dynamic p oblems, such as managing he sys em's
masses, ine ias, ac ua o limi s, and ex e nal o ces (Chose e al., 2005). I also conside s he
empo al aspec o mo ion planning. T ajec o y planning uses he pa h ob ained om pa h
planning ha indica es he posi ion and o ien a ion o poin s in ca esian space and join space
and de e mines he ime p o iles o posi ion, eloci y, and accele a ion o each link, which
a e hen p o ided o he con olle s wi hin he obo ’s con ol sys em. The complexi y o
mo ion planning inc eases wi h he numbe o deg ees o eedom (DOF) in he obo . As he
numbe o pa hs be ween he s a and goal posi ion inc eases, so does he numbe o
ajec o ies, making he p oblem signi ican ly mo e challenging and equi ing g ea e
compu a ional powe . A scheme illus a ing how obo mo ion planning wo ks can be shown
in Figu e 14.
32
Figu e 14 – Schema ic ep esen a ion o obo mo ion planning. Adap ed om (S. Liu & Liu, 2020).
I is impo an o highligh ha he gene a ed planning can occu in wo di e en
spaces: Ca esian Space (also known as Task Space o Ope a ional Space) and Join Space o
Con igu a ion Space. The ope a ional space e e s o he h ee-dimensional ca esian space
ha de ines he posi ion and o ien a ion o a obo ’s end-e ec o . The join space is de ined
by a ec o o join coo dina es, whose componen s a e he ansla ional and angula
displacemen s o each join o a obo ic link. Usually, planning mo emen s in Ca esian space
equi es less compu a ional e o because he ajec o ies a e de ined by posi ion and
o ien a ion coo dina es. In con as , he join space has a highe dimensionali y, as i depends
on each join o he obo . Since hese join s a e independen , he sea ch o a mo ion solu ion
in ol es a la ge sea ch space (Gulle a e al., 2020).
Rega ding he ope a ional and join spaces, he wo kspace is de ined as he subse o
he ask space ha he end-e ec o 's ame can each. In o he wo ds, he wo kspace o a
manipula o is desc ibed as a se o poin s ha can be eached by i s end-e ec o and depends
on he leng h o he links and he join limi s. The wo kspace can u he be decomposed in o
Reachable Space, which consis s o he olume o he wo kspace ha he obo can each
om a leas one o ien a ion, and dex e ous space, which is he olume o he wo kspace ha
he obo end-e ec o can each in any o ien a ion. The dex e ous wo kspace is a speci ic pa
o he eachable wo kspace. By de aul , when calcula ing he wo kspace o a manipula o , he
end-e ec o is dic a ed by he end o he las link o he obo . Howe e , depending on he
ask, he end-e ec o can a y. Fo example, in he MIAR P ojec , he manipula o needs o
g asp a se o boxes, so he end-e ec o , in his case, is he g ippe . The eby, he wo kspace
depends on he ool- ame ans o ma ion (Figu e 15) ha is a ached o he ip o he
manipula o (C aig, 2017).
33
Figu e 15 - The ep esen a ion o a obo 's ool ame in ela ion o he base ame. Adap ed om (C aig, 2017).
3.2 Mo ion Planne s U ilized in he MIAR P ojec
Selec ing he mos app op ia e mo ion planning algo i hm is necessa y o a obo ic
manipula o o execu e collision- ee pa hs success ully. Howe e , he selec ion o he mos
sui able planne is a di icul assignmen since he e a e nume ous e ec i e s a egies
a ailable o mo ion planning p oblems. The e isn’ a single global planning algo i hm sui able
o e e y ype o mo ion planning p oblem, and all he me hods ha e hei weaknesses and
s eng hs (Lynch & Pa k, 2017). When selec ing a mo ion planning me hod o obo ic sys ems,
se e al c i ical ac o s mus be conside ed o ensu e he me hod is app op ia e o a speci ic
applica ion (LaValle, 2006). These ac o s include: ajec o y dis ance, sho e ajec o ies
o en lead o as e ask comple ion; execu ion ime, minimizing cycle ime di ec ly impac s
p oduc i i y in indus ial se ings; compu a ional complexi y, ce ain algo i hms ha e longe
p ocessing imes, which can slow down he en i e sys em; planning app oach, whe he i
in ol es c ea ing a solu ion based on he obo ’s en i onmen be o e he ajec o y is ini ia ed
o building he ajec o y dynamically as he obo mo es; obo ’s dynamic cons ain s; and
he na u e o he obs acles, whe he he obs acles a e igid o de o mable (Gomes De B i o,
2018).
As al eady s a ed, he main ocus o his disse a ion is o de elop legible mo ions o
a edundan manipula o in in e nal logis ics asks, so he selec ion o he ideal mo ion planne
34
is a opic o c ucial impo ance in he de elopmen o his wo k. The manipula o has o
ope a e in a es ic ed space whe e he placemen o he boxes in he access amps p esen s
a signi ican challenge. As a esul , i is equi ed o c ea e a ull ajec o y ep esen ing all he
ope a ions o pick o place, conside ing all he obs acles wi hin he manipula o ’s wo kspace
ha could a ec i s planning. Gi en he na u e o hese en i onmen s, a global mo ion planne
is used o execu e he in ended asks.
Al hough he collabo a i e manipula o will ope a e in an en i onmen sha ed wi h
human ope a o s, i will no pe o m collabo a i ely di ec ly wi h hem. In o he wo ds, he
manipula o will no di ec ly in e ac wi h he agen s a ound i . Hence, his p ojec excludes
he use o human-like planne s, as he p ima y goal is o gene a e sa e and smoo h ajec o ies
o he manipula o while ensu ing i can comple e asks in he sho es ime possible, which
is c i ical o mee wo k deadlines. Human-like planne s a e ypically slowe and demand
g ea e compu a ional esou ces, making hem less sui able o his applica ion.
The global planne s used in his p ojec a e he RRT, RRT-Connec , RRT*, T-RRT, Bi-
TRRT, PRM*, LazyPRM*, P ojEST, BiEST, and KPIECE. The planne s will be p esen ed in mo e
de ail nex , excep o he RRT, RRT-Connec , and RRT* planne s, which ha e al eady been
analyzed in Chap e 2.3.
3.2.1 PRM*
PRM* is an ad anced e sion o he s anda d sampling-based mo ion planning
algo i hm PRM designed o ind op imal pa hs in high-dimensional con igu a ion spaces. This
ex ended me hod app oaches op imali y by sys ema ically inc easing he numbe o
connec ion a emp s as he oadmap expands. As al eady explained, he P obabilis ic
Roadmap s a egies gene a e nodes h ough andom samples o he obo ’s con igu a ion
space. While PRM connec s each node o i s nea es neighbo s om a ixed adius, PRM* uses
a sphe e wi h a connec ion adius o each newly sampled node. The adius o hese sphe es
is scaled loga i hmically based on he numbe o neighbo ing nodes a ound he new node
(Ka aman & F azzoli, 2011). This me hod ensu es ha e e y node is linked o enough
neighbo s, acili a ing he disco e y o sho e pa hs. The e o e, his app oach makes he
oadmap by connec ing he nodes wi hin he speci ied adius. The algo i hm uses g aph sea ch
echniques, like Dijks a's o A* algo i hms, o ind he sho es pa h be ween he s a and
goal con igu a ions wi hin he oadmap. In his planne , he phases o building he oadmap
35
and sea ching occu simul aneously, and like he RRT* planne , PRM* is also conside ed
asymp o ic op imali y (Alandes, 2015).
3.2.2 LazyPRM*
The LazyPRM* is an asymp o ically op imal sampling-based mo ion planning algo i hm
ha uses lazy collision checking o enhance pa h inding e iciency in high-dimensional
con igu a ion spaces, meaning ha i only de e s collision checks on an edge when i is pa o
a po en ial candida e pa h. As he name sugges s, his is a e sion o PRM* (Hause , 2015).
While PRM* pe o ms collision checks du ing he oadmap cons uc ion phase, leading o
highe compu a ional cos s, Lazy PRM in eg a es lazy collision checking. S ill, i does no
gua an ee op imali y, LazyPRM* inco po a es lazy s a e alidi y checking in o he PRM*
planne . This algo i hm c ea es andom nodes, and each node is connec ed o i s neighbo s
based on a connec ion adius o disco e op imal pa hs. Unlike PRM*, he edges be ween he
nodes a en´ immedia ely checked o collisions. Edges a e assumed o be ini ially alid and
a e checked only when a candida e's pa h o he goal is ound. I an edge is de ec ed o be in
collision in he checking, i is emo ed om he oadmap, and al e na i e pa hs a e explo ed.
This s a egy a oids many edges ha canno be on an op imal pa h, signi ican ly educing
compu a ional o e head.
3.2.3 KPIECE
The Kinodynamic Planning by In e io -Ex e io Cell Explo a ion (KPIECE) algo i hm (I.
Sucan & Ka aki, 2008) is a sampling-based mo ion planne speci ically designed o handle
sys ems wi h complex dynamics. Unlike he as majo i y o planne s, which equi e explici
s a e sampling, KPIECE p ojec s he high-dimensional s a e space on o a one o mul i-le el
g id-based disc e iza ion, c ea ing a se o cells ha ep esen di e en egions o he space.
This disc e iza ion guides he planne in es ima ing he co e age o he s a e space and allows
o iden i ying unde explo ed a eas. Since KPIECE is a ee-based planne , i c ea es a ee o
mo ion om he ini ial s a e ha g ows h ough he cells, connec ing easible new s a es. As
new s a es a e added, KPIECE upda es he co e age in o ma ion o he co esponding cells
and adjus s i s explo a ion s a egy o concen a e on a eas o he g id wi h less co e age.
Du ing he explo a ion, he algo i hm dis inguishes be ween in e io cells, su ounded by
explo ed cells, and ex e io cells, which a e on he bounda y o he explo ed egions. By aking
36
p e e ence on ex e io cells, KPIECE expands he bounda ies o he explo ed space, p omo ing
a comple e explo a ion. The p ocess con inues un il a pa h om he ini ial s a e o he goal
egion is ound.
3.2.4 T-RRT
The T ansi ion-based Rapidly Explo ing Random T ee (T-RRT) is a sampling-based
mo ion planning algo i hm ha compu es pa hs in high-dimensional cos spaces by combining
andomized pa h planning and s ochas ic op imiza ion me hods (Jaille e al., 2010). This is an
ex ended e sion o he RRT algo i hm, which u ilizes he explo a o y s eng hs o he planne
o na iga e h ough he space. T-RRT inco po a es a s ochas ic ansi ion es o guide he
explo a ion owa d lowe -cos a eas wi hin he obo 's con igu a ion space. T-RRT uses his
ansi ion es o decide whe he o accep o ejec new po en ial s a es o he g owing ee
based on he cos unc ion a ia ion ela i e o he local mo ion ha connec s he cu en
s a e o he new po en ial s a e (Figu e 16). The cos unc ion conside ed in he cos map can
ep esen a ious c i e ia, such as ene gy consump ion o he dis ance o maximize be ween
he obo and su ounding objec s o c ea e pa hs wi h high clea ance. The e o e, T-RRT
a o s solu ions ha minimize he accumula ed cos , leading o pa hs ha a e conside ed no
only easible bu also sa e. The planne also has a empe a u e pa ame e ha is dynamically
adjus ed h ough he sea ch p ocess and in luences he accep ance p obabili y o s a es. A
each accep ed uphill ansi ion, his pa ame e is dec eased o a oid o e -explo ing in egions
o high cos , and in case he uphill ansi ion be ween he s a es is ejec ed, he empe a e is
inc eased o help he explo a ion o ind new po en ial s a es (De au s e al., 2013). Thus, his
algo i hm s a s by ini ializing a ee wi h an ini ial con igu a ion and se ing he ini ial
empe a u e pa ame e . The algo i hm samples a andom s a e, and he exis ing ee
a emp s o ex end owa d he sampled s a e, gene a ing a po en ial new one. The cos o he
new s a e is compa ed o he cos o he pa en s a e, and he ansi ion es de e mines he
accep ance p obabili y based on he cos di e ence. I he new s a e is accep ed, i is added
o he ee. A he same ime, he empe a u e pa ame e is adjus ed based on he success
a e o he s a e ansi ion, allowing he algo i hm o adap dynamically o he cos map. This
p ocess epea s un il he ee eaches he goal s a e. Compa ed o he RRT planne , he T-RRT
p oduces be e pa hs because he RRT explo es he con igu a ion space o ind easible pa hs
bu doesn’ conside a cos unc ion. On he o he hand, T-RRT isn’ asymp o ically op imal,
37
meaning i doesn´ con e ge owa ds an op imal solu ion like he RRT* planne , which aims
o ind he sho es pa h in con igu a ion space by con inuously e ining i s ee s uc u e.
Ne e heless, T-RRT o e s as e and mo e easible pa hs in high-dimensional spaces han
RRT*, which can ake ime o ind a solu ion.
Figu e 16 - Example o a cons uc ion p ocess o he T ansi ion-based RRT planne . The ed zones ep esen high cos a ea
o he cos map. Adap ed om (Jaille e al., 2010).
3.2.5 Bi-TRRT
The Bidi ec ional T ansi ion-based Rapidly Explo ing Random T ee (Bi-TRRT) is an
adap ion o he T-RRT algo i hm ha me ges he ad an ages o bidi ec ional sea ch wi h cos -
sensi i e explo a ion (De au s e al., 2013). Simila o he RRT-Connec planne , Bi-TRRT
conside s wo g owing ees, one oo ed om he ini ial con igu a ion and he o he om he
goal s a e, and ies o connec hem. Each ee explo es he cos map independen ly and has
i s own empe a u e pa ame e . The algo i hm al e na es be ween g owing each ee. A each
i e a ion, one o he ees a emp s o ex end owa d a sampled andom s a e o he
con igu a ion space. Then, he ansi ion es de e mines whe he he new s a e is accep ed
o ejec ed based on he cos di e ence be ween he new and he pa en s a e. I he new
s a e passes he ansi ion es , i is added o he ee, and he o he ee ies o expand
owa d his new node. I he ees a e unable o connec , hey swi ch oles, and he p ocess is
epea ed. This p ocess con inues wi h he ees al e na ely expanding owa d andomly
sampled s a es un il he junc ion is made. While RRT* gene ally con e ges o be e solu ions
compa ed o Bi-TRRT, he la e o en disco e s solu ions mo e quickly.
38
3.2.6 BiEST
Expansi e Space T ees (EST) is a ee-based mo ion planning algo i hm buil o obo s
wi h many DoFs ha inc emen ally builds a oadmap h ough he con igu a ion space,
a o ing he explo a ion o less explo ed a eas h ough he concep o isibili y (Hsu e al.,
1997). The planne comp ises he expansion and connec ion phases, which a e i e a i ely
execu ed. In he expansion phase, a node in he ee is selec ed o expansion based on i s
weigh unc ion, which is de ined by he numbe o sampled con igu a ions wi hin i s
neighbo hood up o a speci ied dis ance h eshold. Nodes wi h lowe weigh s, indica ing
ewe nea by con igu a ions, a e p io i ized o expansion. This ensu es he ee g ows owa d
less explo ed a eas, p e en ing epea ed explo a ion o al eady co e ed egions and
encou aging expansion in o new di ec ions. Then, andom s a es a e sampled in he
neighbo hood o he selec ed node o he ee. The g oup o nodes nea he ee node ha
can connec in a s aigh line wi hou encoun e ing obs acles is called he isibili y se
(Alandes, 2015). The planne connec s hose sampled con igu a ions ha con ibu e o he
isibili y egion wi h he ee node, leading o he expansion o he ee. Then, he p ocess
epea s. In he connec ion phase, he algo i hm ies o connec he ee o he goal
con igu a ion. I he connec ion is no possible, he ee con inues o expand. While he PRM
planne gene a es andom nodes h oughou he con igu a ion space and ies o connec
hem, la e sea ching o he bes pa h be ween he ini ial and goal nodes, he EST planne
ocuses i s explo a ion solely on he ele an space egions o each he solu ion. This
app oach allows he EST o a oid unnecessa y compu a ion when c ea ing a oadmap o he
en i e con igu a ion space. The e o e, his planne EST is ideal o single-que y pa h planning
p oblems and is well sui ed o en i onmen s wi h na ow passages.
The BiEST algo i hm is a bidi ec ional e sion o he EST planne ha explo es he
con igu a ion space by g owing wo ees simul aneously, one om he s a con igu a ion
and ano he om he goal con igu a ion. Fo each ee, i expands owa d he node wi h he
lowes weigh , and andom con igu a ions a e sampled. The ee expands owa d he
con igu a ions wi hin he isibili y egion o he selec ed node. The wo ees g ow owa d
each o he , and when he isibili y egion o one o he ees in e sec s wi h he o he , he
planne a emp s o connec he newly added nodes. The isibili y egion o a ee is he union
o he isibili y egions o all i s nodes. As he wo ees g ow owa d each o he , he
39
explo a ion space dec eases, allowing he BiEST planne o ind solu ions mo e quickly han
he EST planne .
3.2.7 P ojEST
The P ojec ion-based Expansi e Space T ee algo i hm (P ojEST) is an ex ended e sion
o he EST planne ha inco po a es a p ojec ion unc ion o map he high-dimensional s a e
space in o a lowe -dimensional space (Hsu e al., 1997). This p ojec ion enables P ojEST o
impose a g id on he p ojec ed space, allowing i o ocus he expansion o he ee in
unde explo ed a eas. The algo i hm selec s nodes o expansion based on a weigh unc ion,
p io i izing egions ha a e less densely sampled, and uses he p ojec ion o guide he
sampling and connec ion o he nodes nea he ee. The planne uses a de aul p ojec ion
associa ed wi h he s a e space i no p ojec ion is de ined. The algo i hm a emp s o connec
he ee, which oo s om he ini ial node, o he goal con igu a ion, i e a ing un il a alid
pa h is disco e ed. By educing he dimensionali y o he p oblem du ing explo a ion, P ojEST
can con e ge on solu ions mo e quickly han he s anda d EST planne .
3.3 Ha dwa e Componen s
The obo ic a m de ined o he mo ion planning asks in he scope o he MIAR p ojec
is he collabo a i e manipula o KUKA LBR iiwa 14 R820 (Figu e 17). This is a edundan
manipula o wi h 7 deg ees o eedom. A manipula o is conside ed kinema ically edundan
when i has mo e deg ees o eedom han hose s ic ly necessa y o pe o m a gi en ask.
Manipula o s wi h 7 DoF a e gene ally edundan , which allows o g ea e manipulabili y. The
eason o using his ype o obo in he case s udy is p ima ily due o i s edundancy, which
enables mo e p ecise and dex e ous mo emen s. This is bene icial o pe o ming asks and
allowing he obo ic a m o exhibi smoo he and legible mo emen s. The edundan deg ee
o eedom allows he manipula o o pe o m seconda y asks beyond achie ing a speci ic
posi ion and o ien a ion, such as a oiding obs acles. The 7-DoF an h opomo phic obo
ea u es an S-R-S kinema ic s uc u e consis ing o a sphe ical shoulde , a o a ional elbow,
and a sphe ical w is (Fa ia e al., 2018).
46
Acco ding o Figu e 17, he angle θ1𝑣 is loca ed on he xy plane since he obo ’s i s
join o a es a ound he ho izon al plane. To ob ain he angle, i is necessa y o de e mine he
dis ance om he obo ’s shoulde o i s w is . As he posi ion and o ien a ion o he obo ’s
ip a e known due o he gene al homogenous ans o ma ion ma ix and he ec o om he
base o he shoulde is 𝑝
02=[0 0 𝐿1], because he link 1 only o a es axially, hen he ec o
om he shoulde o he ip is compu ed by he Equa ion 3.11.
𝑝
27= 𝑝
07− 𝑝
02
3.11
Since he ec o om he w is o he obo ’s ip is 𝑝
67=[0 0 𝐿4] and he eal
o ien a ion be ween hese wo ames can be acqui ed by he o a ion ma ix R
07 de i ed
om T
07, as p esen ed abo e in Equa ion 3.2, he shoulde -w is ec o is calcula ed using he
Equa ion 3.12.
𝑝
26= 𝑝
27− 𝑝
67 R
07
3.12
The θ1 angle, posi ioned in he xy-plane, es ablishes he x and y coo dina es o he ip
and, consequen ly hose o he w is , and is hus in luenced by 𝑝
26,𝑥 and 𝑝
26,𝑦. Howe e , in
case he ec o 𝑝
26 is colinea wi h he s anda d uni ec o in he di ec ion o he x-axis
[0,0,1], which means ha he w is o he obo is aligned wi h he shoulde di ec ion, hen
θ1𝑣 is unde ined because 𝑝
26,𝑥 and 𝑝
26,𝑦 a e ze o. This scena io ep esen s a singula i y. To
add ess his issue, when such a condi ion a ises, θ1𝑣 akes he alue 0. This condi ion is e i ied
by he c oss p oduc o bo h colinea ec o s, which mus be 0 (Equa ion 3.13).
θ1𝑣 ={𝑎𝑡𝑎𝑛2(𝑝
26,𝑦,𝑝
26,𝑥), 𝑖𝑓 ‖𝑝
26×[0 0 1]‖>0
0, 𝑖𝑓 ‖𝑝
26×[0 0 1]‖=0
3.13
As shown in Figu e 20, he i ual join θ2𝑣 is based on he p ojec ion o he shoulde -
w is ec o on he z-axis and he xy-plane, bu i also depends on he angle Ф, he la e being
de e mined by he law o cosines (Equa ion 3.14).
47
Ф=a ccos(𝑑𝑠𝑒2+‖𝑝
26‖2−𝑑𝑒𝑤2
2 𝑑𝑠𝑒 ‖𝑝
26‖)
3.14
Figu e 20 - Illus a ion o he i ual manipula o used o calcula e FK. Adap ed om (Fa ia e al., 2018).
Depending on whe he he elbow o he obo is upwa ds o downwa ds, he alue o
θ2𝑣 will di e . Tha being said, ano he pa ame e , called Global Con igu a ion (GC), is
conside ed. This pa ame e is associa ed wi h speci ic join s and akes a alue o 1 i he join 's
con igu a ion is posi i e and -1 o he wise. In his case, i he elbow is up (θ4> 0), he GC will
be 1, and i he elbow is down, he GC will be -1 (Equa ion 3.15).
θ2𝑣= a an2(√𝑝
26,𝑥2+ 𝑝
26,𝑦2,𝑝
26,𝑧)+𝐺𝐶4Ф
3.15
Wi h he i ual angles known, he i ual posi ion o he obo 's shoulde ( 𝑝
04𝑣) can be
de e mined by applying he p e iously desc ibed FK p ocess o ob ain he homogeneous
ans o ma ion ma ix T
04𝑣. Gi en ha , he shoulde and w is posi ions a e iden ical in bo h
he eal and i ual con igu a ions, as seen in Figu e 19, he ec o s linking he base o he
shoulde ( 𝑝
02 and 𝑝
02𝑣) and he base o he w is ( 𝑝
06 and 𝑝
06𝑣) a e he e o e equi alen . The
only di e ence lies in he ec o s linking he base o he elbow ( 𝑝
04and 𝑝
04𝑣) owing o he
di e en elbow posi ions in he eal and i ual manipula o s. As he a m angle is de ined as
48
he angle be ween he wo planes: SEW and SEW , he pa ame e will be compu ed by
calcula ing he angle be ween he no mal ec o s o hese planes.
The c oss-p oduc o wo ec o s spawns a ec o ha is o hogonal o bo h. The no mal
ec o o he plane SEW can be de e mined by he c oss-p oduc o he ec o s belonging o
he plane, namely he ec o s linking he shoulde o he elbow ( 𝑝
24) and he elbow o he
w is ( 𝑝
26) (Equa ion 3.18).
𝑝
24= 𝑝
04− 𝑝
02
3.16
𝑝
26= 𝑝
06− 𝑝
02
3.17
𝑉𝑆𝐸𝑊= 𝑝
24× 𝑝
26
3.18
The no mal ec o o he plane SEW is h ough he ec o s 𝑝
24𝑣 and 𝑝
26𝑣 (Equa ion 3.21).
𝑝
24𝑣= 𝑝
04𝑣− 𝑝
02𝑣
3.19
𝑝
26𝑣= 𝑝
06𝑣− 𝑝
02𝑣
3.20
𝑉𝑆𝐸𝑊𝑣= 𝑝
24𝑣× 𝑝
26𝑣
3.21
Be o e o mula ing he a m angle, i is impo an o ind whe he he pa ame e is
posi i e o nega i e. The c oss p oduc o he no mal ec o s de ined in Equa ions 3.18 and
3.21 gene a es a ec o ha is collinea wi h he ec o ha connec s he shoulde o he w is
(𝑝
26). I hese ec o s ha e he same di ec ion, he sign o he a m angle is posi i e, o he wise,
i is nega i e. To conclude, he a m angle esul s om he do p oduc o he wo no mal
ec o s VSEW and VSEW (Equa ion 3.22).
Ѱ=𝑠𝑖𝑔𝑛Ѱ a ccos(𝑉𝑆𝐸𝑊𝑣
∙𝑉𝑆𝐸𝑊
)
3.22
49
3.3.2 In e se Kinema ics
The in e se kinema ics (IK) consis s o inding he join alues o he obo based on
he posi ion and o ien a ion coo dina es o he end-e ec o , ha is, he e is a con e sion om
he ca esian space o he join space. As p e iously indica ed, 7-DOF manipula o s a e
gene ally edundan , and his edundancy p oblem is add essed in he IK. As he a ge pose
is speci ied by six a iables ( h ee o posi ion and h ee o o ien a ion), i becomes necessa y
o sol e a sys em o six nonlinea equa ions in ol ing se en unique a iables co esponding
o he obo ic a m's join s. This esul s in an inde e mina e sys em, indica ing ha he in e se
kinema ics p oblem is unde -cons ained. Fa ia e al. (2018) p oposed an analy ical app oach
o sol ing he in e se kinema ics o 7-DOF manipula o s designed o p e en join limi s and
singula i ies. Fo his pu pose, beyond he coo dina es o he desi ed pose, he pa ame e s
a m angle (Ѱ) and global con igu a ion (GC) a e in oduced as inpu s o he p oblem. Thus,
sol ing he a m's in e se kinema ics equi es hese h ee a iables, whe eby o a gi en a ge
pose, he desi ed a m angle is speci ied, along wi h he GC alues o he shoulde , elbow, and
w is join s ( alues o 1 o -1), indica ing whe he θ2, θ4, and θ6 a e posi i e o nega i e. In IK
o 7-DOF manipula o s, he e a e eigh possible solu ions o a speci ic hand pose and known
a m angle: ou wi h he elbow (θ4) ben backwa d and ano he ou wi h he elbow ben
o wa d. Wi hin each o hese eigh con igu a ions, he e is an in ini y o possibili ies in he
null space due o he se en h deg ee o eedom, which allows con inuous mo emen s o he
obo wi hou a ec ing he end-e ec o ’s pose.
Acco ding o Fa ia e al. (2018), o de e mine he eal join s o he obo , i is necessa y
o i s calcula e he alue o join θ4, as i is he only join independen o he a m angle
pa ame e . As such, by applying he Equa ion 3.12 again, i ´s possible o ha e he eal
shoulde -w is ec o . Since he shoulde posi ion doesn’ change ela i e o he base, he
ec o 𝑝
02 emains he same as he i ual one, he ec o 𝑝
07 is de i ed om he desi ed
posi ion, he ma ix R
07 is es ablished using he desi ed o ien a ion o he obo ’s end-
e ec o (Yaw, Pi ch, Roll) and he Roll-Pi ch-Yaw ans o ma ion ma ix (Equa ion 3.4), and
he ec o 𝑝
67 is once again he ec o ha links he w is o he end-e ec o by he z-axis.
Thus, based on Figu e 20, he angle θ4 is achie able h ough he law o cosines. As
men ioned ea lie , in he IK, he GC is an inpu ha desc ibes he obo 's con igu a ion. Since
he emaining join angles depend on he upwa d o downwa d o ien a ion o he obo 's
50
elbow, i is essen ial o in oduce he GC4 pa ame e in Equa ion 3.23 o speci y whe he θ4
will be posi i e o nega i e.
θ4=𝐺𝐶4a ccos(‖𝑝
26‖2−𝑑𝑠𝑒2−𝑑𝑒𝑤2
2 𝑑𝑠𝑒 𝑑𝑒𝑤 )
3.23
In o de o disco e he o he join angles, he eal manipula o ´s elbow posi ion mus
be ound. To accomplish his, i is i s calcula ed he pose o he i ual elbow, using he
p ocess p e iously applied in he FK, whe eby θ1𝑣, Ф angle and θ2𝑣 a e de e mined wi h he
help o Equa ions 3.13, 3.14 and 3.15. I is impo an o emind ha he alue o he i ual
join θ3𝑣 is ze o. The pose o he i ual elbow is dic a ed by he T
03𝑣 o T
04𝑣 ma ices h ough
he D-H con en ion, whe e R
03𝑣 o R
04𝑣 ep esen he o ien a ion o he ames in he elbow
p esen ed in he Figu e 18.
Conside ing ha he a m angle de ines he angle be ween he eal a m con igu a ion
and i s i ual/non- edundan con igu a ion, he eal elbow pose will co espond o he i ual
elbow pose when o a ed by an Ѱ angle a ound he axis passing h ough he elbow and w is
(Equa ion 3.24).
𝑅
03= 𝑅
0Ѱ 𝑅
03𝑣
3.24
Gi en his logic, Rod igues's o a ion o mula can be used o con e he i ual elbow pose o
he eal elbow pose. The Rod igues's o a ion o mula allows he o a ion o he ec o s om
he o a ion ma ix a ound a speci ied axis by a gi en angle (Equa ion 3.25).
R=I3+(sin𝜑) 𝐾+ (1−cos(𝜑)) 𝐾2
3.25
, whe e I3 is he iden i y ma ix, 𝜑 is he o a ion angle a ound he axis, and K is he c oss-
p oduc ma ix associa ed wi h he uni ec o k, ha ep esen s he o a ion axis. Applying
his o mula o he case s udy esul s in he ollowing Equa ion 3.26.
𝑅
0Ѱ=I3+(sinѰ) [𝑝
26
×]+(1−cos(Ѱ)) [𝑝
26
×]2
3.26
51
Replacing he Equa ion 3.26 on he Equa ion 3.24, 𝑅
03 can be o mula ed as ollows:
𝑅
03=𝐴𝑠sin(Ѱ)+𝐵𝑠cos(Ѱ)+ 𝐶𝑠
3.27
, whe e:
𝐴𝑠=[𝑝
26
×] 𝑅
03𝑣
𝐵𝑠=−[𝑝
26
×]2 𝑅
03𝑣
𝐶𝑠=[𝑝
26
𝑝
26
𝑇] 𝑅
03𝑣
The ma ix 𝑅
03 can also be exp essed using he Dena i -Ha enbe g con en ion (Equa ion
3.28) h ough he mul iplica ion o T
01, T
12 and T
23, as p e iously de ailed.
R
03
=[cos(𝜃1)cos(θ2)cos(𝜃3)− 𝑠𝑖𝑛(θ1) 𝑠𝑖𝑛(θ3) cos(𝜃1) 𝑠𝑖𝑛(θ2)cos(𝜃3) 𝑠𝑖𝑛(θ1)+cos(𝜃1)cos(θ2)sin(𝜃3)
cos(𝜃1) 𝑠𝑖𝑛(θ3)+cos(𝜃2)cos(θ3)sin(𝜃1)𝑠𝑖𝑛(θ1) 𝑠𝑖𝑛(θ2)cos(𝜃2)sin(θ1)sin(𝜃3)− 𝑐𝑜𝑠(θ1) 𝑐𝑜𝑠(θ3)
−𝑠𝑖𝑛(θ2) cos(𝜃3) cos(𝜃2)−𝑠𝑖𝑛(θ2) 𝑠𝑖𝑛(θ3)]
3.28
By analyzing he ma ix 𝑅
03, i can be obse ed ha θ2 can be de e mined as ollows:
θ2=a ccos (𝑎𝑠32sin(Ѱ)+ 𝑏𝑠32cos(Ѱ)+𝑐𝑠32)
3.29
Based on Equa ion 3.29, and aking in o conside a ion he signal o θ2 gi en by he global
con igu a ion pa ame e (GC2), i can be concluded ha he eal join θ2 can be exp essed as
ollows:
θ2=GC2 a ccos (𝑎𝑠32sin(Ѱ)+ 𝑏𝑠32cos(Ѱ)+𝑐𝑠32)
3.30
Applying he same logic, i is possible o de e mine he alues o he join s θ1 and θ3, which
depend on θ2 .
52
θ1=a an2(GC2 [𝑎𝑠22sin(Ѱ)+ 𝑏𝑠22cos(Ѱ)+𝑐𝑠22],GC2 [𝑎𝑠12sin(Ѱ)
+ 𝑏𝑠12cos(Ѱ)+𝑐𝑠12])
3.31
θ3=a an2(GC2 [−𝑎𝑠33sin(Ѱ)− 𝑏𝑠33cos(Ѱ)−𝑐𝑠33],GC2 [−𝑎𝑠31sin(Ѱ)
− 𝑏𝑠31cos(Ѱ)−𝑐𝑠31])
3.32
The calcula ion o he emaining join s o he obo will depend on 𝑅
03, which can now
be de e mined since he join s θ1, θ2, and θ3 a e known; on 𝑅
07, which is de ined by he
obo 's pose, as es ablished in Equa ions 3.4 and 3.10; and on 𝑅
34, which is ob ained om he
ma ix 𝑇
34, p esen ed in Equa ion 3.3, and he alue o join θ4, which is now known. Wi h all
hese ma ices ecognized, he ma ix 𝑅
47 can be exp essed by Equa ion 3.33.
𝑅
47= 𝑅
34𝑇 𝑅
03𝑇 𝑅
07
3.33
Following he same easoning p esen ed ea lie o he ep esen a ion o he 𝑅
03 ma ix, 𝑅
47
can be exp essed as ollows:
𝑅
47=𝐴𝑤sin(Ѱ)+𝐵𝑤cos(Ѱ)+ 𝐶𝑤
3.34
, whe e:
𝐴𝑤= 𝑅
34𝑇 𝐴𝑠𝑇 𝑅
07
𝐵𝑤= 𝑅
34𝑇 𝐵𝑠𝑇 𝑅
07
𝐶𝑤= 𝑅
34𝑇 𝐶𝑠𝑇 𝑅
07
Gi en he algeb aic o a ion ma ix 𝑅
47 (Equa ion 3.35), de i ed om he homogeneous
ma ix 𝑇
47, and conside ing he global con igu a ion pa ame e o he manipula o 's w is
(GC6), join θ6, ollowed by join s θ5 and θ7, can be de e mined using Equa ions 3.36, 3.37
and 3.38, espec i ely.
R
47
=[cos(𝜃5)cos(θ6)cos(𝜃7)− 𝑠𝑖𝑛(θ5) 𝑠𝑖𝑛(θ7) −cos(𝜃7) 𝑠𝑖𝑛(θ5)−cos(𝜃5)cos(θ6)sin(𝜃7)cos(𝜃5) 𝑠𝑖𝑛(θ6)
cos(𝜃5) 𝑠𝑖𝑛(θ7)+cos(𝜃6)cos(θ7)sin(𝜃5)cos(𝜃5)cos(θ7)− 𝑐𝑜𝑠(θ6) 𝑠𝑖𝑛(θ5) 𝑠𝑖𝑛(θ7) 𝑠𝑖𝑛(θ5) 𝑠𝑖𝑛(θ6)
−𝑠𝑖𝑛(θ6) cos(θ7) 𝑠𝑖𝑛(θ6) 𝑠𝑖𝑛(θ7)cos(𝜃6)]
3.35
53
θ6=GC6 a ccos (𝑎𝑤33sin(Ѱ)+ 𝑏𝑤33cos(Ѱ)+𝑐𝑤33)
3.36
θ5=a an2(GC6 [𝑎𝑤23sin(Ѱ)+ 𝑏𝑤23cos(Ѱ)+𝑐𝑤23],GC6 [𝑎𝑤13sin(Ѱ)
+ 𝑏𝑤13cos(Ѱ)+𝑐𝑤13])
3.37
θ7=a an2(GC6 [𝑎𝑤32sin(Ѱ)+ 𝑏𝑤32cos(Ѱ)+𝑐𝑤32],GC6 [−𝑎𝑤31sin(Ѱ)
− 𝑏𝑤31cos(Ѱ)−𝑐𝑤31])
3.38
In summa y, i can be concluded ha he calcula ion o he join s o he edundan 7-
deg ee-o - eedom obo depends on he desi ed pose, as well as on he a m angle and he
global con igu a ion pa ame e s.
3.4 So wa e Tools
Fo he de elopmen o his p ojec , a se o so wa e ools was u ilized. Acco dingly, his
sec ion begins wi h a b ie in oduc ion o he ROS2 amewo k. Nex , i explo es he Mo eI
lib a y, which is used o mo ion planning in obo ic sys ems, es ablishes i s ela ionship wi h
he OMPL lib a y and highligh s Gazebo and RViz plugins. Finally, his chap e p esen s he
physical simula o CoppeliaSim and he so wa e Au odesk Fusion.
3.4.1 ROS2 Middlewa e
One o he mos impo an ools o ake in o conside a ion in his wo k is he Robo
Ope a ing Sys em (ROS) amewo k. ROS is an open-sou ce amewo k consis ing o
communica ion ools and a se o plug-and-play lib a ies ha aid in c ea ing complex sys ems.
ROS is conside ed a specialized middlewa e o obo ics, p o iding communica ion
in as uc u e, ha dwa e abs ac ion, low-le el de ice con ol, exchange o messages
be ween p ocesses, and mo e (Se ano, 2015). Al hough i is independen o he ype o
p og amming language used, ROS p ima ily u ilizes C++ and Py hon o i s de elopmen
(Figu e 21).
54
Figu e 21 - Languages used in ROS communica ion ools. Adap ed om (The Robo ics Back-End, 2018).
ROS was c ea ed o acili a e code euse in obo ics esea ch and de elopmen . I
ea u es an in eg a ed eposi o y ha allows use s o u ilize p e-exis ing code o a ious
obo ic applica ions. ROS suppo s a wide ange o obo ic componen s, including ae ial,
g ound, humanoid, and unde wa e obo s, as well as di e en ypes o senso s, such as GPS
ecei e s. As such, i se es as a pla o m ha enables he in eg a ion o a ious so wa e ools
wi h di e en pu poses, such as OpenCV and Mo eI . Fo ins ance, ROS can be in eg a ed wi h
OpenCV o enable da a cap u ed by came as o be p ocessed by ad anced algo i hms o mo e
e icien image p ocessing, such as objec de ec ion, mo ion acking, and pa e n ecogni ion
(Se ano, 2015).
In he MIAR P ojec , ROS was used o connec he selec ed mo ion planne o he
edundan manipula o ’s mo emen s in he logis ics asks and he physical so wa e ha
se es as a obo ic simula ion en i onmen . In his p ojec , he ope a ing sys em used is
Ubun u 22.04, and he ecommended ROS dis ibu ion is ROS2 Humble Hawksbill. ROS2
Humble is an ad anced e sion o he ROS amewo k.
Re aining some ROS concep s is impo an o ensu e a co ec unde s anding o he
s eps aken in he p ojec in Chap e 4.
3.4.1.1 ROS S uc u e
ROS can be di ided in o wo kspaces con aining packages. Each package can con ain
small p og ams called nodes, which enable connec ions be ween di e en sys ems.
3.4.1.1.1 ROS Wo kspace
A ROS wo kspace is a di ec o y ha s a s emp y and c ea es a speci ic s uc u e when
buil using he Colcon build ool. I includes a sou ce (s c) subdi ec o y con aining he sou ce
code o he ROS packages. Addi ionally, he wo kspace has h ee o he di ec o ies: he build
di ec o y, whe e in e media e iles a e s o ed; he ins all di ec o y, whe e all c ea ed packages
55
a e ins alled; and he log di ec o y, which holds a ious logging in o ma ion abou he builds
made in he wo kspace.
3.4.1.1.2 Packages
Packages a e he basic uni o so wa e o ganiza ion in ROS. Each package can con ain
lib a ies, execu ables, o sc ip s, which a e used o s uc u e and modula ize he code.
Packages can be c ea ed using ei he CMake o Py hon, allowing a wo kspace o include
packages o di e en build ypes. Figu e 22 illus a es a wo kspace s uc u e con aining a
CMake package de eloped in C++ and a Py hon package de eloped in Py hon, bo h loca ed in
he sou ce olde .
Figu e 22 - Wo kspace wi h CMake and Py hon packages.
3.4.1.1.3 Nodes
A node is an execu able ile ha pe o ms compu a ion. Nodes a e c ea ed inside
packages. These p ocessing uni s a e independen and can communica e wi h o he nodes.
(Ta a es, 2015). Figu e 23 shows an example o a obo ics applica ion composed o nodes.
This sys em consis s o h ee ROS packages, each con aining a se o nodes ini ia ed sepa a ely
and communica ing wi h each o he .
62
Figu e 29 depic s he high-le el sys em a chi ec u e o he mo e_g oup node, which is
a cen al componen in Mo eI . This ROS node ope a es as an in eg a o , coo dina ing
di e en componen s o o e a se o ROS ac ions and se ices o use s. The e a e h ee
p ima y ways o access he se ices and ac ions o mo e_g oup: mo e_g oup_in e ace
package, which p o ides a simple and e ec i e C++ in e ace ha communica es wi h he
mo e_g oup node ia ROS opics, se ices, and ac ions. I enables unc ionali y o mos asks
a use may need, such as de ining he a ge ’s pose, mo ion planning, adding objec s in he
en i onmen , and a aching o de aching objec s om he obo ; mo ei _commande
package h ough Py hon; Via a G aphical In e ace, using he mo ion planning plugin o R iz,
he ROS isualiza ion ool. R iz is a 3D isualize designed o he ROS en i onmen (da Cos a,
2019). I allows he display o senso da a and he obo ’s s a e in eal- ime, p o iding a i ual
model o he obo . I p esen s senso da a h ough ROS opics and se ices, which helps
unde s and he obo 's pe cep ion o i s en i onmen . This simula o is mainly used o alida e
planning solu ions in i ual en i onmen s, usually wo king in pa allel wi h he physical
so wa e Gazebo, be o e being applied o he eal obo . I enables isualiza ion o he obo 's
ajec o y, helping o iden i y po en ial issues. Gazebo is a 3D simula o designed o ec ea e
en i onmen s o mul iple obo s. I includes dynamic and kinema ic physics o accu a ely
simula e eal-wo ld condi ions such as ic ion, damping, and o he en i onmen al ac o s.
The desc ip i e obo o ma used in Gazebo is he Simula ion Desc ip ion Fo ma (SDF). As
he R iz, Gazebo is used o es and alida e obo ic beha io s be o e eal ope a ions. (Koenig
& Howa d, 2004)
The mo e_g oup e ie es di e en ypes o in o ma ion om he ROS pa ame e
se e : he obo _desc ip ion pa ame e , which p o ides he obo ’s URDF ile, and he
obo _desc ip ion_seman ic pa ame e , which p o ides he obo ’s SRDF ile. I also sea ches
o o he Mo eI con igu a ion da a like join limi s, kinema ics, mo ion planning se ings, and
pe cep ion in o ma ion. These con ig iles a e also gene a ed wi hin he Mo eI con ig
package o he obo by he Mo eI Se up Assis an .
63
Figu e 29 - High-le el sys em a chi ec u e o he Mo eI mo e_g oup node. Adap ed om (PickNik Robo ics, 2024a).
In Mo eI , e en i he ajec o y has al eady been planned o a gi en ask, i s ill needs
o be execu ed. To do so, Mo eI uses con olle s o execu e he ajec o y o ce ain
ha dwa e. The os2_con ol amewo k s anda dizes he in e ac ion be ween he obo
ha dwa e and he so wa e con olle s (Amadi e al., 2024). I p o ides a lexible in e ace o
con ol di e en ypes o ha dwa e, whe he o eal obo s, physical simula ions, o mock
se ups. This amewo k comp ises he con olle manage node, he con olle s equi ed o
ajec o y execu ion, and ha dwa e in e aces. The con olle manage node manages
con olle swi ching by ac i a ing, deac i a ing, and loading con olle s as needed. I connec s
he con olle s o he equi ed ha dwa e in e aces and manages Mo eI by ac i a ing he
app op ia e con olle s. The use s can also access he con olle manage h ough ROS
se ices. The con olle s a e plugins based on con ol heo y ha e alua e inpu commands
and calcula e ou pu s o con ol obo join s. The mos used con olle plugins a e he
join _ ajec o y_con olle , which con ols he ajec o ies o obo join s; he
join _s a e_con olle , which publishes he s a us o obo join s; and he posi ion, eloci y,
and e o con olle s, which send he desi ed posi ion, eloci y, and e o commands,
espec i ely, o he ha dwa e in e ace. As men ioned ea lie , hese con olle s a e con igu ed
in he os2_con olle s.yaml ile. The ha dwa e in e ace is used o send and ecei e
commands om he ha dwa e. The e a e se e al ha dwa e in e aces, he mos common
being he Join Command In e ace, which suppo s join con ol, and he Join S a e In e ace,
which suppo s eading he s a e o he join s (posi ion, eloci y, e o ). In case he ha dwa e
in e ace o a obo in Mo eI doesn’ al eady exis , he use can c ea e i s own.
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Se e al ha dwa e plugins a e a ailable ega ding he ha dwa e wi h which Mo eI can
communica e. Among hese s ands he eal ha dwa e o a obo ha co esponds o he
obo ’s sys em in e ace and he gazebo_ os2_con ol/GazeboSys em, which in eg a es he
con ol o he obo wi h he Gazebo simula o , allowing ealis ic physical simula ions. I he
goal is o simula e he obo ’s beha io wi hou elying on a physical simula o o he eal
obo , ake ha dwa e can be used in Mo eI h ough he mock_componen s/Gene icSys em
plugin. This plugin is mainly used o o line es ing o he os2_con ol amewo k, as i
simula es ideal obo beha io by mi o ing commands o hei s a es. Since in he p ojec ,
he alida ion es s o he ajec o ies gene a ed om he manipula o we e no o be
suppo ed by he Gazebo physical simula o , hen he Gene icSys em plugin was used.
To isualize a obo in Mo eI , as well as plan and execu e i s mo ions, ROS 2 launch
iles a e equi ed. The Py hon launch iles handle he loading o all he con igu a ion
pa ame e s p esen in he mo ei _con ig package. To achie e his, Mo eI uses he
Mo eI Con igsBuilde u ili y o load hese pa ame e s, which include he obo desc ip ion
and seman ic desc ip ion iles (URDF and SRDF), mo ion planning and kinema ics plugins,
ajec o y execu ion se ings, and o he necessa y con igu a ions. Once he Mo eI
con igu a ion pa ame e s a e loaded, he mo e_g oup node mus be launched o ini ia e he
Mo e G oup C++ In e ace. I ’s also impo an o launch he 2 lib a y o manage coo dina e
ans o ms, especially he s a ic ans o m publishe node, which es ablishes he s a ic
ans o m be ween he obo ’s base and wo ld ames. The obo s a e publishe node mus
be launched o ead he obo ’s join s a es, compu e ame ans o ma ions using he URDF
ile, and publish hese ans o ms o 2. Finally, he os2_con ol amewo k mus be se up
o he obo o execu e a ajec o y. To s a he os2_con ol, he con olle manage node
mus be launched and spawn he equi ed con olle s and he ha dwa e plugin needed o he
ajec o y execu ion.
3.4.3 CoppeliaSim
Al hough Mo eI does pe o m mo ion planning o he manipula o o he a ious pick-
and-place ope a ions, i is essen ial o alida e he planning es s be o e applying hem o eal-
wo ld scena ios. To do his, he mo emen s mus i s be simula ed in a dynamic analysis.
While Gazebo is he simula o ha ypically wo ks alongside Mo eI , his p ojec will u ilize
CoppeliaSim o e i y he a m's mo emen s in a digi al en i onmen .
65
CoppeliaSim (Figu e 30) is a physical simula o ha aids he de elopmen and alida ion
o planning algo i hms and obo ic sys ems (Bogae s e al., 2020). This so wa e allows he
c ea ion o any obo and he design o complex en i onmen s wi h mul iple obo s. I includes
a physical engine ha enables obo ic beha io s ha a e mo e simila o eal solu ions.
The selec ion o CoppeliaSim o his p ojec is due o i s compa ibili y wi h a ious
ope a ing sys ems, including Windows and Linux, making i sui able o wo k in Ubun u 22.04,
which is he equi ed e sion o he p ojec . CoppeliaSim also suppo s he c ea ion o obo ic
models in he wo king en i onmen by impo ing CAD iles such as s l, and can also ead URDF
iles like in Mo eI . This compa ibili y allows he same obo model o be used in bo h Mo eI
and he physical simula o . Fu he mo e, CoppeliaSim can also es ablish ex e nal
communica ion wi h o he so wa e because i ’s compa ible wi h ROS. These s eng hs make
i a e sa ile ool o connec ing he mo ion planning o he obo ic a m in Mo eI wi h he
obo 's physical model in CoppeliaSim.
CoppeliaSim is o ganized in o models, which a e indi idual elemen s ha can ep esen
a obo , senso s, o e en a pe son, and a scena io, which comp ises all he models ha
compose he simula ion space. Each model is ep esen ed by a hie a chy ee ha includes
he physical model, which conside s all he physical p ope ies, such as mass and momen s o
ine ia, and he g aphical model, which is associa ed wi h he isual ep esen a ion o he
model in he scena io. The ee can also ha e join s connec ing he model wi h any o he
scena io componen . CoppeliaSim allows he con ol o di e en models by associa ing hem
wi h child sc ip s. The p op ie a y language o hese sc ip s is Lua o Py hon.
In his wo k, CoppeliaSim eplica es he manipula o 's mo emen du ing he pick-and-
place ope a ions h ough ROS and alida es he planned mo ions by ec ea ing a digi al win
o he obo ’s wo kspace.
66
Figu e 30 - CoppeliaSim in e ace.
3.4.4 Au odesk Fusion
Las ly, Au odesk Fusion was used, which is a Compu e -Aided Design (CAD), Compu e -
Aided Enginee ing (CAE), and Compu e -Aided Manu ac u ing (CAM) so wa e de eloped by
Au odesk. This so wa e (Figu e 31) allows use s o de ine and model a ious componen s, se
p ope ies, and assemble di e en models. I also helps alida e p oduc s by subjec ing hem
o s a is ical, he mal, dynamic, and o he analyses. In he con ex o his wo k, Au odesk
Fusion was u ilized o model he access amps and any o he essen ial componen s o he
obo 's wo kspace du ing he planning o he pick-and-place ope a ions. Addi ionally, he
so wa e was used o simula e he pe o mance o he cus om inge s designed o he
selec ed g ippe o he obo , as de ailed in Sec ion 4.4.2.
Figu e 31 - Au odesk Fusion In e ace.
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4 De eloped Wo k
The p esen chap e encompasses he p ac ical elemen s unde aken in he de elopmen o
his p ojec . The chap e begins wi h a desc ip ion o he sys em a chi ec u e o he MIAR
p ojec , emphasizing he module whe e his disse a ion i s. I hen add esses he c ea ion o
he simula ion model o he obo ic a m’s wo kspace and he selec ion o a sui able g ippe
o he desi ed ope a ions, including he de elopmen o cus omized g ippe inge s.
Fu he mo e, i ou lines he con igu a ion and con ol o he se : manipula o and g ippe o
Mo eI and he in eg a ion wi h he CoppeliaSim so wa e. The las sec ion exposes he
implemen a ion o mo ion algo i hms o he obo ic a m’s pick-and-place ope a ions.
4.1 Sys em A chi ec u e
As p e iously indica ed, his disse a ion is pa o he MIAR p ojec , whose objec i e is
o anspo Ta ge s om an in e media e s o age bu e o supply amps. Thus, de eloping a
sys em a chi ec u e encompassing se e al modules was necessa y. Figu e 32 illus a es he
global a chi ec u e o he MIAR sys em.
Figu e 32 - Global a chi ec u e o he MIAR sys em.
This a chi ec u e is cen e ed a ound he co e module, Flee Managemen , which is
esponsible o managing he lee o ehicles and con ains a map o he p oduc ion lines'
supply a ea. This module ecei es da a om he p oduc ion lines h ough he Bosch sys em
68
and ansmi s he in o ma ion o each ehicle ia he local module Se ice Manage . This
module ecei es he se ice o he Flee Managemen and di ides i in o asks ha a e sen o
he Task Manage . This submodule is wi hin he Mo emen Con olle Module, which includes
se e al submodules dedica ed o con olling he AMR and planning he manipula o ’s
mo emen s. The ask manage ensu es he p ope execu ion o assigned asks by ac i a ing
he app op ia e submodules in he co ec sequence. The a chi ec u e also includes he
En i onmen Pe cep ion local module ha comp ises se e al submodules esponsible o
acqui ing and p ocessing senso y in o ma ion, ei he h ough LiDAR o he ision sys em. This
disse a ion ocuses p ima ily on he A m Planning submodule, which is asked wi h planning
and con olling he a m’s mo emen s. Howe e , de eloping his submodule equi es
unde s anding he mobile manipula o 's condi ions. This includes a clea de ini ion o he
asks o be pe o med by he mobile manipula o and i s wo kspace du ing he ope a ions.
4.2 Simula ion Model
As p e iously men ioned, he main aim o his wo k is o de elop sa e and smoo h
ajec o ies o he KUKA LBR iiwa 14 R820 manipula o . The espec i e a m is moun ed on
he KUKA KMR iiwa 14 mobile pla o m. In he Bosch Ca Mul imédia BRgP shop loo , he
Ta ge s a e posi ioned on op o dollies, which a e anspo ca s used o mo e loads wi hin
he acili y. The Ta ge s a e manually ans e ed om he dollies o di e en assembly lines
by PoUPs, a designa ion es ablished o he ope a o s esponsible o he speci ic ask. The
objec i e o he MIAR p ojec 's "To Be" challenge is o eplace hese PoUPs wi h au onomous
mobile manipula o obo s o pe o m he ask. An example o he in ended wo k layou is
shown in Figu e 33.
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Figu e 33 - In ended wo k layou a Bosch Ca Mul imedia B gP.
As can be seen in Figu e 33, he blue zone co esponds o he ini ial loca ion o he dollies
loaded wi h hei espec i e Ta ge s.
Fi s , he mobile pla o m mus mo e o he Dolly Supply zone so ha he obo ic a m
can pick up he Ta ge s and place hem on op o he pla o m. A e wa d, he pla o m mo es
o he di e en wo ks a ions, ep esen ed in yellow in Figu e 33, allowing he a m o deli e
he Ta ge s o he app op ia e s a ions. I 's impo an o no e ha he co ido s whe e he
au onomous mobile manipula o obo s ope a e a e 1.2 me e s wide, which limi s hei
mo emen du ing he execu ion o he desi ed asks. The co ido nex o Dolly Supply is
wide , allowing mobile pla o ms o o a e when picking up boxes.
Se e al p elimina y pa ame e s mus be conside ed o ca y ou he simula ion model,
namely he maximum numbe o Ta ge s posi ioned on op o he dollies ha he a m can
each and he maximum numbe o Ta ge s ha he mobile pla o m can anspo om he
Dolly Supply o he di e en wo ks a ions. The selec ion o he g ippe o he obo ic a m is
also ex emely impo an o he manipula ion o he Ta ge s.
The eby, some undamen al elemen s equi ed o ec ea e he in ended wo k layou
a he Bosch Ca Mul imedia BRgP shop loo we e modeled using Au odesk Fusion so wa e.
These elemen s include he access amps and he dolly channel. O he essen ial componen s,
like he Ta ge s and he dollies, we e p o ided as CAD iles by Bosch.
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The e a e wo ypes o Ta ge s o be manipula ed, bo h o which a e plas ic PP
con aine s om he U z G oup (U z G oup, 2014). One con aine is la ge , measu ing 600 x
400 x 220 mm, while he o he is smalle , measu ing 400 x 300 x 220 mm. Bo h con aine s
ha e loose lids. Figu e 34 p esen s hese con aine s and hei co esponding CAD models.
Figu e 34 – Con aine s-RAKO om U z G oup and hei espec i e CAD models.
In his disse a ion, he la ge con aine s will be e e ed o as "600x400 boxes" and
he smalle ones as "400x300 boxes" based on he ou e dimensions o hei bases (Figu e 35).
(a)
(b)
Figu e 35 - (a) Ou e dimensions o he base o he la ge con aine ; (b) Ou e dimensions o he base o he smalle
con aine .
Simila o he Ta ge s, he e a e wo ypes o dollies, each designed o a speci ic kind
o con aine . Cu en ly, he dollies a e posi ioned oge he a he Dolly Supply wi hou any
secu e mechanism o hold hem in place (Figu e 36).
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Figu e 36 - Dolly Supply zone o MIAR P ojec .
As a esul , he dolly channels a e used o e ain and guide he espec i e dollies. An
example o his mechanism, along wi h i s CAD model, can be seen in Figu e 37.
Figu e 37 – Dolly Channel and CAD ep esen a ion.
Finally, he access amps a e esponsible o s o ing he boxes o a ce ain pe iod o
ime. In he cu en shop loo , he amps ha e ei he wo le els, which include an uppe and
a lowe le el, e e ed o as one-le el amps, o h ee le els, consis ing o an uppe , middle,
and lowe le el, e e ed o as wo-le el amps. The uppe and middle le els a e designa ed
o holding ull boxes om he Dolly Supply p o ided by he PoUP, while he lowe le el
con ains he emp y boxes le by he human ope a o s. The CAD models o he one and wo-
le el amps can be checked in Figu e 38 and Figu e 39, espec i ely. The e a e wo ypes o
amps co esponding o each kind o Ta ge , whe e he wid h o each le el o he amp is he
box leng h wi h an addi ional 10 mm, implying high p ecision in he picking and placemen o
he boxes. Appendix A shows hese ou amps wi hou he olle ails in mo e de ail.
Fo his p ojec , he one-le el amps will be used o he pick-and-place ope a ions.
Thus, he mobile manipula o has o place he boxes e ie ed om he Dolly Supply on he
uppe le el o he amps, pick he emp y boxes om he lowe le els, and anspo hem back
o he Dolly Supply.
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Based on he applied me hod, he mos app op ia e solu ion was he 2FGP20 g ippe
om OnRobo (Figu e 44). This g ippe can communica e using ROS, which is bene icial o
in eg a ing wi h he mo ion planning so wa e Mo eI , which is esponsible o planning he
obo 's ajec o ies.
Figu e 44 - 2FGP20 on iew (dimensions in mm). Adap ed om (OnRobo , 2023).
4.4 De elopmen o he G ippe Finge s
As s a ed in Sec ion 4.3, one o he equi emen s is ha he g ippe mus ha e a minimum
dis ance be ween i s inge s g ea e han 400 mm o g asp he boxes success ully. Al hough
he s oke o he 2FGP20 g ippe is 260 mm, i s opening is insu icien o g abbing he Ta ge s.
To ensu e e ec i e manipula ion o bo h boxes, i is essen ial o de elop cus om g ippe
inge s. Using Au odesk Fusion so wa e, he desi ed inge s we e modeled, and h ough a
Fini e Elemen Analysis (FEA), he inge s we e es ed o e i y whe he hey could mee he
equi emen s o be used in a eal applica ion. The FEA me hod is use ul o simula ing and
iden i ying causes o ailu e in mechanical sys ems o p e en ailu es be o e manu ac u ing.
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4.4.1 Modeling he G ippe Finge s
Typically, pa allel g ippe inge s a e composed o simple pla es ha apply p essu e o
he manipula ed objec . The angen ial componen o he applied p essu e mus be su icien
o each a s a ic equilib ium, balancing he g a i a ional o ce and p e en ing he objec om
alling. Howe e , he boxes unde s udy ea u e a g oo e co esponding o hei ou e mos
su ace, which has a hickness o only 6 mm, as can be seen in Figu e 45, which illus a es he
p o ile iew o bo h Ta ge s.
Figu e 45 - P o ile iew o bo h Ta ge s wi h he ou e dimensions.
To add ess his, he g ippe inge s we e inspi ed by how a human hand ypically g asps hese
ypes o boxes. The inge s we e designed in an L shape, allowing hem o comp ess and
handle he boxes, as shown in Figu e 47. This design app oach educes he p essu e equi ed
on he ou e su aces o he box by applying load componen s in bo h he ho izon al and
e ical di ec ions. As de ailed in Figu e 45, he g oo e wid h is 15 mm, which means he
minimum ape u e o he 400x300 boxes mus be 370 mm. To ensu e a sa e g ip, he design
o he inge s allows a dis ance o 368 mm when he g ippe is closed. This design enables he
g ippe o clamp he boxes in 2 mm i necessa y (Figu e 46). When he g ippe is open, he
dis ance be ween he inge s eaches 628 mm because he g ippe 's s oke is 260 mm. This
esul s in a o al clea ance o 28 mm in ela ion o he 600x400 boxes. Consequen ly, high
p ecision is equi ed when planning he g asping and eleasing ope a ions o he obo . The
dimensions o each inge can be e i ied in Appendix B. In he CAD model, ille s we e applied
80
o he pe pendicula su aces whe e he boxes a e g asped, aiming o educe s ess
concen a ions and acili a e mesh gene a ion.
(a)
(b)
Figu e 46 – (a) Maximum G ippe Ape u e; (b) Minimum G ippe Ape u e.
One o he main p oblems o he 2FGP20 g ippe is ha i s lange is decen alized 50
mm in ela ion o i s cen e , as epo ed in Figu e 44. Ano he issue is ha only one o he
g ippe inge s is mo able. Since he wo boxes o be manipula ed ha e a leng h di e ence o
200 mm i bo h inge s ha e he same leng h, a signi ican misalignmen would occu be ween
he g ippe ’s lange and he cen e o one o he boxes. Such misalignmen is undesi able, as
i could c ea e a momen du ing manipula ion asks ha migh comp omise he obo 's
ope a ions. To mi iga e his p oblem, he inge s mus ha e di e en sizes. The e o e, he
leng h o each inge was adjus ed in e ac i ely un il easonable dimensions we e achie ed.
This ensu es ha he dis ance om he obo lange o he cen e o each box isn´ oo
di e en . Since hese inge s a e in ended o ini ial es s, one o he Bosch equi emen s was
ha hey should be made o PLA.
Figu e 47 - G ippe holding he wo ypes o Ta ge s.
4.4.2 E alua ion and simula ion o he inge s
A e c ea ing he geome ic model o he inge s, he p e-p ocessing o a linea s a ic
analysis was made, whe e inpu s like he ma e ials, mesh, and loading condi ions we e
81
es ablished. Rega ding loads, he inge s we e subjec ed o wo o ces: a ho izon al o ce
ep esen ing he maximum g ipping o ce o 400 N and a e ical o ce co esponding o he
maximum weigh o he Ta ge s. This la e o ce is esponsible o p o oking ensile s esses
in he uppe su ace o he inge s and comp essi e s esses in he lowe su ace. Since he
wo inge s wi hs and he boxes o 8 kg, an ac ing o ce o 39.24N was applied o he inne
su aces o each inge . Rega ding bounda y condi ions, each inge is ixed o he claws a he
base o he g ippe , which cons ains all six deg ees o eedom (DoF) o he model.
The mesh is a c ucial ac o o conside , as i s quali y signi ican ly impac s he
simula ion esul s. A highe mesh densi y, which means mo e elemen s by uni o olume,
leads o mo e accu a e esul s. Howe e , highe compu a ion cos s will be equi ed i he
mesh is oo e ined. Since each inge is oluminous, solid elemen s we e conside ed,
speci ically quad a ic e ahed al elemen s. These elemen s a e composed o 4 co ne nodes,
6 mid-side nodes, and 6 edges. Second-o de elemen s gene ally yield mo e ealis ic esul s
han linea elemen s because hey can ha e cu ed edges o be e cap u e geome ic
cu a u es. This ea u e was conside ed in he mesh gene a ion (Figu e 48).
Figu e 48 - P e-p ocessing o he mobile g ippe inge .
Ins ead o using local mesh e inemen , whe e local mesh con ols a e applied o di e en
egions o he model, an adap i e mesh e inemen was used. In his me hod, he sol e
au oma ically iden i ies c i ical s ess egions and e ines he mesh by employing smalle
elemen s in hose a eas. As he mesh densi y inc eases, he s ess le els end o ise un il he
esul s s abilize. F om ha poin , u he mesh e inemen does no yield signi ican
di e ences in he esul s. A con e gence s udy was conduc ed o achie e wha is known as a
con e ged mesh. This me hod in ol es successi ely e ining he mesh un il he change in a
c i ical pa ame e , usually s ess, be ween wo consecu i e i e a ions is less han a ce ain
82
pe cen age (Madie , 2021). In his case, a pe cen age o 5% was se . To a oid excessi e
compu a ional imes du ing he mesh gene a ion, a maximum o 6 i e a ions was de ined
(Figu e 49).
Figu e 49 - Mesh gene a ion pa ame e s in Au odesk Fusion.
Following p e-p ocessing, he inge s we e subjec ed o s a ic analysis o de e mine
hei abili y o suppo he applied loads du ing he g asping ac ions. Due o he high applied
loads, a sa e y ac o o 4:1 based on c i ical anspo a ion was conside ed o compa ison
(PHD Inc., 2001). In he pos -p ocessing phase, he esul s we e analyzed. Based on he esul s
ob ained, i can be concluded ha he inge s can wi hs and he applied loads, as he alues
o s ess, s ain, and displacemen a e low, and he sa e y ac o is high h oughou he pa .
As expec ed, he maximum s ess and s ain occu on he pe pendicula in e nal su aces due
o he momen gene a ed by he g ipping o ce. The maximum displacemen is obse ed a
he ips o he inge s, as his g ipping o ce is signi ican ly g ea e han he weigh o he box.
Mo eo e , he s ess on he mo able inge (Figu e 50 – (a)) is sligh ly highe han ha on he
ixed inge (Figu e 50 – (b)) because he mo able inge is longe , esul ing in a g ea e
momen a i s ip.
83
(a)
(b)
Figu e 50 – (a) S a ic simula ion on he mo able inge ; (b) S a ic simula ion on he ixed inge .
Gi en he high sa e y ac o , i ´s possible o unde s and ha he inge s we e o e -
dimensioned. The design can be op imized o educe he weigh o he inge s. A shape
op imiza ion was conside ed, as shown in Figu e 51. Howe e , since hese inge s we e
in ended solely o ini ial es ing, his s udy has no been conduc ed. The e o e, he inge s
used we e hose desc ibed ea lie , wi h a o al weigh o 1 kg.
84
Figu e 51 - Finge s shape op imiza ion.
Fo sa e y p ecau ions, he s udy was also conduc ed on he boxes o de e mine i hey
could wi hs and he g ippe 's maximum g ipping o ce, which can each high le els. As
an icipa ed, he maximum g ipping o ce did no impac he boxes (Figu e 52). Gi en ha he
maximum expe ienced s ess is 3.1 MPa, i can be concluded ha he box emains wi hin he
elas ic egime and doesn´ su e plas ic de o ma ion because he box has a yield s ess o
30.30 MPa.
Figu e 52 - S a ic simula ion o he boxes o be manipula ed.
4.4.3 Finge s Tes
The inge s we e manu ac u ed using 3D p in ing, and manipula ion es s using a
Doosan obo we e conduc ed a Eu opneumaq acili ies o alida e he simula ions. The es s
demons a ed ha he g ippe could success ully g asp he wo ypes o boxes (Figu e 53).
85
(a)
(b)
Figu e 53 - (a) G ip es o he 400x300 box; (b) G ip es o he 600x400 box.
In his p ojec , he g ippe moun ed wi h he designed inge s has a o al weigh o
4.7kg. Al hough, a i s glance, i appea s ha he a m can anspo he boxes since he o al
weigh o be handled is 12.7 kg, his doesn’ necessa ily mean ha he a m can manipula e
he maximum weigh o he Ta ge s. As p e iously men ioned, he heigh o he g ippe mus
no be oo la ge because i would a ec he a m’s desi ed pe o mance. This limi a ion
happens because he payload o he a m a ies depending on he dis ance om he
manipula o 's moun ing lange o he cen e o g a i y o he objec being manipula ed, as
depic ed in Figu e 54.
Figu e 54 - Payload diag am o KUKA LBR iiwa 14 R820 manipula o . Adap ed om (KUKA, 2019).
Due o he signi ican di e ence in weigh be ween he g ippe and he box, i can be
in e ed ha he cen e o g a i y o his sys em would be loca ed somewhe e wi hin he
86
Ta ge . By analyzing he payload diag am, i is e iden ha o he manipula o o wo k wi h
he G ippe +Ta ge sys em, he alue o Lz mus be less han app oxima ely 100 mm.
Howe e , he g ippe heigh alone al eady exceeds his alue, as shown in Figu e 44.
The e o e, i is concluded ha e en hough he g ippe mee s he ini ial p ojec equi emen s,
i s conside able dis ance om he lange o i s base ine i ably educes he payload capaci y
o he a m.
4.5 Maximum Numbe o Ta ge s o be Manipula ed
Since he Kuka LBR iiwa 14 R820 obo ic a m is moun ed on op o he mobile pla o m
and gi en he ac ha a dolly a he Bosch ac o y loo can suppo mo e han one Ta ge , i
is impo an o de e mine he maximum numbe o Ta ge s he obo ic a m can each. An
analysis was conduc ed o he mobile pla o m in di e en posi ions, concluding ha he
maximum numbe o Ta ge s ha he obo ic a m can g asp om he dolly is ou (Figu e 55).
Beyond ou boxes, he a m canno g asp any addi ional Ta ge s om abo e.
(a)
(b)
Figu e 55 – (a) Manipula o g asping he i s box om he dolly; (b) Maximum numbe o Ta ge s placed on a dolly ha he
a m can each.
Ano he c ucial aspec o conside in he s udy is he maximum numbe o Ta ge s he
mobile pla o m can anspo o he wo ks a ions. This numbe depends on he obo ic a m's
abili y o place he boxes along he pla o m. Since he Ta ge s o be handled can ha e wo
di e en dimensions, he analysis was ca ied ou o h ee dis inc cases: he maximum
numbe o 600x400 boxes placed on he base o he mobile pla o m, he maximum numbe
o 400x300 boxes ha can be placed on he base o he pla o m, and he maximum numbe
o Ta ge s comp ising bo h ypes o dimensions. Fo he i s case, i was de e mined ha wo
87
600x400 boxes could no ully i on he base o he KMR. Addi ionally, he a m can only place
wo s acked boxes due o i s con igu a ion, which does no allow o he addi ion o a hi d
box (Figu e 56).
Figu e 56 – S udy o he maximum numbe o 600x400 boxes on he pla o m.
Rega ding he 400x300 boxes, a ious dis ibu ions o hese boxes a he pla o m's
base we e examined o de e mine which would allow o he maximum numbe o boxes. I
was obse ed ha he KMR could anspo 4 boxes (Figu e 57).
Figu e 57 - S udy o he maximum numbe o 400x300 boxes on he pla o m.
In he las case, di e en dis ibu ions we e also conside ed o he wo ypes o boxes.
I was concluded ha only wo 400x300 boxes and wo 600x400 boxes could be anspo ed
(Figu e 58).
94
Figu e 66 - KUKA LBR iiwa 14 R820 wi h 2FGP20 g ippe in R iz.
4.6.2 Mo eI -CoppeliaSim Communica ion
In Mo eI , when a obo is execu ing a ajec o y o a speci ic poin , i s join s, including
he g ippe join , a e always ead by he /join _s a es opic. To a oid ajec o y e o s in
CoppeliaSim, i is essen ial o he obo o eplica e he same join mo emen s as in Mo eI
wi hou any delay. Hence, ROS2 communica ion was made be ween he wo so wa e. The
communica ion logic ollowed he diag am in Figu e 67, whe e CoppeliaSim sends he poses
o mul iple objec s in he manipula o 's wo kspace o Mo eI , while Mo eI con inuously
sends he obo 's join alues o CoppeliaSim.
Figu e 67 – Mo eI -CoppeliaSim Communica ion Diag am.
95
A node named /join _s a e_subsc ibe was c ea ed o subsc ibe o he /join _s a es
opic, eading he obo ’s join alues ha a e p o ided in he senso _msgs/msg/Join S a e
message, which con ains da a desc ibing he s a e o he con olled join s in Mo eI , including
he join names, posi ions, and eloci ies ( os2.o g, 2020). This node publishes he obo join s
o a new opic whose message ype is eadable in CoppeliaSim. Fo his pu pose, he message
ype: s d_msgs::msg::S ing was used. In he CoppeliaSim MIAR p ojec scena io, a child sc ip
associa ed wi h he obo ic a m was made. This sc ip subsc ibed o he newly c ea ed opic
and applied he join posi ions in eal ime o he CoppeliaSim manipula o .
To synch onize he opening and closing o he g ippe join in CoppeliaSim wi h i s
coun e pa in Mo eI , a opic named echa _g ippe was c ea ed in he main code and was
esponsible o execu ing he g ippe ’s inge mo emen . Each ime he g ippe is commanded
o g asp o elease an objec in Mo eI , he g ippe 's join posi ion is se as he message o be
published on his opic. In CoppeliaSim, he g ippe ’s child sc ip subsc ibes o his opic, eads
he join posi ion, and applies i as he alue o i s join .
To plan he obo ’s mo emen in Mo eI , he a m mus be awa e o he obs acles
a ound i o de ec hem and p o ide collision- ee ajec o ies. To sol e his p oblem, e e y
model in CoppeliaSim ha impac s he manipula o ’s wo kspace ecei ed a child sc ip . This
sc ip eads he models' poses ela i e o he a m's base ame and publishes hem in a opic,
wi h o ien a ion gi en in qua e nion o ma . To make hese objec s appea in he R iz
en i onmen , a se o code was de eloped o ead he poses om he opics associa ed wi h
each CoppeliaSim model and collision objec s we e c ea ed by eading he models' s l iles o
gene a e meshes. The objec s we e hen published o he /collision_objec Mo eI opic,
which is esponsible o placing objec s in R iz. In Table 5, i is possible o isualize he message
ypes along wi h he associa ed opics ha acili a e communica ion be ween he wo
so wa e.
96
Table 5 - Topics and messages used o he Mo eI -CoppeliaSim communica ion.
Topic
Message
Goal
/join _s a es
senso _msgs/msg/Join S a e
Used o know he s a es o
he obo ’s join s.
/join _s a e_s ing
s d_msgs/msg/S ing
Publishes he obo ’s join
posi ions o CoppeliaSim.
/ echa _g ippe
s d_msgs/msg/S ing
Sends he g ippe join
posi ion in he g asp and
elease ac ions.
/caixa400_300_posi ion_o ien a ion
geome y_msgs/msg/Pose
Sends he pose o he
objec s loca ed in he
obo ’s wo kspace.
/caixa400_300_posi ion_o ien a ion_1
/caixa400_300_posi ion_o ien a ion_2
/caixa400_300_posi ion_o ien a ion_3
/caixa600_400_posi ion_o ien a ion
/caixa600_400_posi ion_o ien a ion_1
/caixa600_400_posi ion_o ien a ion_2
/caixa600_400_posi ion_o ien a ion_3
/ca caca_posi ion_o ien a ion
/pla a o ma_posi ion_o ien a ion
/ ampa1ni el_410_posi ion_o ien a ion
/ ampa1ni el_610_posi ion_o ien a ion
/collision_objec
mo ei _msgs/msg/CollisionObjec
C ea es collision objec s in
R iz en i onmen .
Fo a mo e de ailed unde s anding, Appendix C p o ides a isualiza ion o how he
communica ion is es ablished be ween he nodes and opics esponsible o sending he
manipula o ’s join s om Mo eI o CoppeliaSim. The nodes and opics in ol ed in sending
he poses o he objec s in he CoppeliaSim simula ion scena io o R iz a e p esen ed in
Appendix D. These connec ions we e ob ained using he ROS ool q _g aph, whe e he nodes
a e ep esen ed by an o al o ma and he opics by a ec angle.
The di e ence in he poses gene a ed by he wo so wa e in ela ion o he wo ld
ame can signi ican ly comp omise he a m's abili y o manipula e objec s co ec ly in bo h
scena ios. Accu acy e o s in da a ansmission exceeding 14 mm can p e en he a m om
g ipping he boxes p ope ly. I is essen ial ha bo h scena ios a e iden ical. Thus, he URDF,
used o isualize he manipula o wi h he g ippe a ached in R iz, was u ilized o c ea e hem
97
in he CoppeliaSim en i onmen . This ensu es no di e ences be ween he wo scena ios
(Figu e 68).
Figu e 68 - CoppeliaSim-Mo eI Communica ion.
4.7 Ramp Analysis and Op imiza ion
An impo an aspec ha needed o be s udied be o e s a ing he pick-and-place
ope a ions was o con i m whe he he “as is” access amps would enable he manipula o o
pick he boxes. A s udy was ca ied ou o in es iga e his si ua ion.
Conce ning he wo-le el amps, i was con i med ha his ype o amp is unsui able
o he pick and place asks. Fo bo h he ope a ions o picking emp y boxes om he lowe
le el and deposi ing ull boxes on he middle le el, he obo ic a m did no ha e con igu a ions
ha would enable i o pe o m hese asks. The dimensions o he se a m and g ippe and
sligh heigh di e ences be ween access le els p e en he manipula o om app oaching he
amp wi hou colliding wi h i . Fu he mo e, due o i s high heigh , he a m canno each o
d op he ull boxes on he uppe le el (Figu e 69). This issue au oma ically limi s he possibili y
o inc easing he heigh be ween he le els.
98
Figu e 69 - A emp o collec o place Ta ge s by he manipula o on he di e en le els o he amp.
Rega ding he one-le el amps, wi h he KMR posi ioned a di e en dis ances om
he 1200 mm co ido , i was concluded ha he edundan manipula o could no pick up
emp y boxes om he lowe le el because he a m links collided wi h he uppe le el (Figu e
70 – (a)). Se e al solu ions we e p oposed o allow he a m o access his ype o amp and
g ab he boxes, such as modi ying he heigh o he amp le els. In an i e a i e p ocess, one-
le el amps wi h di e en heigh le els we e e alua ed based on he dis ance be ween he
KMR and he amps in he co ido . I was concluded ha he lowe le el heigh should no be
educed. Doing so would no only cause e gonomic s ain on he human ope a o s on he
opposi e side o he amp, o cing hem o bend u he o place he boxes, bu would also
comp omise he pa h planning o he manipula o . Lowe ing he le el would equi e he
pla o m o mo e close o he amp so ha he a m could each he box, esul ing in inc eased
di icul y when emo ing he box due o he educed dis ance be ween he pla o m and he
amp. Fo he uppe le el, an inc ease in he heigh o 200 mm was de e mined o p e en he
obo om colliding wi h he amp. Howe e , he heigh could no exceed 300 mm, ega dless
o he pla o m’s dis ance om he amp. This p oposal, howe e , was deemed unsui able
because i would equi e ha all mo ions o emo e he box om he amp be pe o med
using in e se kinema ics (IK) ins ead o a global planne due o he limi ed manipula ion space
ha would signi ican ly inc ease he ime equi ed o he planne o ind a easible solu ion.
This s a egy also would o ce he obo o emo e he boxes om he lowe le el by he side
o he amp, as he e would no be enough clea ance o emo e he box di ec ly be ween he
pla o m and he amp. Ano he sugges ion was o design he amp le els as a s ai case (Figu e
70 – (b)). This design would elimina e he issue o he a m colliding wi h he uppe le el when
picking a box om he lowe le el. Howe e , i would educe he s o age capaci y o he uppe
99
le el and once again c ea e e gonomic disad an ages o he human ope a o s, as he uppe
le el would need o be lowe ed o he a m o each i .
Figu e 70 - (a) Collision o he manipula o 's links wi h he amp uppe le el; (b) P oposed s ai case amp.
I was sugges ed ha he on ba o he uppe le el be cu o acili a e he en y o
he obo ic a m in o he amp o eaching he lowe le el. A he on pa o he uppe le el,
only he olle ails loca ed a he co ne s would emain o suppo he boxes placed a he
le el's en ance. The suppo s uc u e ha holds all he olle ails and connec s hem o he
es o he amp s uc u e would be eposi ioned u he back no o hinde he a m's en y
in o he amp. A s udy was ca ied ou o de ine he op imal en ance cu o he amps,
ensu ing hei sui abili y o he p ojec . F om his s udy, i was concluded ha he ideal amp
o he 600x400 boxes should ha e an en ance cu o 500x350 mm, while he amp o he
400x300 boxes should ha e an en ance cu o 300x350 mm. Besides, bo h amps would
equi e he le els o be aised by 20 cm (Figu e 71).
Figu e 71 - "To be" one-le el amp.
100
Wi h he lowe le el aised by 20 cm, i would be possible o pe o m a m mo emen s
o pick up he box wi hou eso ing o nume ous in e media e in e se kinema ic (IK)
mo emen s. Ano he ad an age is ha he pla o m could be posi ioned a he away om
he amp, enabling di ec emo al o 600x400 boxes om he lowe le el. The inc eased
heigh o he lowe le el in he pick ope a ion would acili a e he placemen planning o he
boxes in he pla o m, as he lowe le el o he amp would be close o he pla o m's base
le el (Figu e 72). Fo picking ope a ions, he pla o m should be posi ioned 455 mm away om
he amps ha s o e he 600x400 boxes and 435 mm om he amps ha hold he smalle
boxes. Fo placing ope a ions, he pla o m mus be se a a dis ance o 185 mm om he
amps. The echnical d awing o he new ype o amp can be seen in Appendix E.
Figu e 72 - Picking he 600x400 box on he op imized amp.
A s udy was also conduc ed o e alua e whe he he p oposed modi ica ions o he
one-le el amps could ende he wo-le el amps sui able o u u e applica ions. In his
scena io, he uppe and middle le els we e designed wi h a cu o 500x350 mm o he
600x400 boxes and a 300x350 mm cu o he 400x300 boxes. Using he o iginal "as is" le el
heigh s, i was obse ed ha he a m s ill collided wi h he le els du ing he placemen asks
(Figu e 73 – (a)). Howe e , i could now each he emp y boxes on he lowe le el (Figu e 73
– (b)).
101
(a)
(b)
Figu e 73 - (a) Collision be ween he obo ic a m and he wo-le el amp wi h en ance cu s; (b) Robo ic a m
e ie ing an emp y box om he wo-le el amp wi h en ance cu s.
Fu he analysis was conduc ed o in es iga e how adjus ing he heigh s o he amp
le els could imp o e hei sui abili y o manipula ion ope a ions. F om his s udy, i was
concluded ha all le els needed o be lowe ed o enable he obo o place boxes on he
uppe and middle le els wi hou collisions (Figu e 74).
Figu e 74 - Box placemen and e ie al ac oss di e en le els o he op imized wo-le el amp.
An example o an op imized wo-le el amp ha suppo s pick-and-place ope a ions is
p esen ed in Figu e 75.
102
Figu e 75 - Example o an op imized wo-le el amp.
Al hough he a m can each all le els o he wo-le el amps, hese amps we e no
conside ed o he pick-and-place ope a ions s udied in his wo k due o issues o spa ial
clu e and he necessi y o educing he heigh o all le els. Such heigh adjus men s would
impose e gonomic s ain on human ope a o s, pa icula ly when placing boxes on he lowe
le el. Mo eo e , o he a m o access he lowe le el, i mus be s e ched, equi ing he
pla o m o be posi ioned close o he amp. This is p oblema ic o la ge boxes, as he
limi ed space be ween he pla o m and he amp would necessi a e eposi ioning he
pla o m u he away om he amp o emo e he box. Thus, execu ing a single
manipula ion ope a ion would equi e addi ional pla o m mo emen s, complica ing he
o e all p ocess.
4.8 Pick-and-Place Ope a ions in Mo eI /CoppeliaSim
In he MIAR p ojec , he e a e eigh manipula ion scena ios o he pick-and-place
ope a ions, ou o which ela e o picking and placing he wo ypes o Ta ge s on he access
amps and ou o which ela e o picking and placing he espec i e Ta ge s on he dollies.
So, eigh ope a ion codes mus be de eloped, each adap ed o he condi ions o i s speci ic
scena io.
103
The co ec execu ion o ajec o ies in he manipula o o he MIAR p ojec was
managed using only wo launch iles. The i s launch ile is esponsible o c ea ing he
Coppelia scena io o Mo eI , and he second is esponsible o execu ing he desi ed ask.
Rega ding he i s launch ile, i is composed o a se o nodes ha a e ini ia ed
sequen ially. Each node ep esen s a p ocess and is de ined by i s execu able, he package i
belongs o, and op ional pa ame e s such as he node name and ou pu . E en handle s we e
used o egis e speci ic ansi ion e en s be ween nodes o ensu e he sequen ial execu ion
o nodes (Open Robo ics, 2024c). This is achie ed using he Regis e E en Handle ac ion along
wi h he OnP ocessExi e en handle . The OnP ocessExi is igge ed when a speci ied node
inishes execu ion, allowing he dependen node o s a only a e i s p edecesso has
inished. This s uc u ed me hod ensu es ha all p ocesses a e execu ed in he co ec o de ,
espec ing dependencies and p e en ing po en ial con lic s du ing execu ion. The i s nodes
in his sequence publish each model p esen in he physical simula o scena io as collision
objec s in R iz. Depending on he numbe o models p esen in CoppeliaSim, he R iz
en i onmen is adap ed o ma ch he simula ion. No hing is published as a collision objec i
he obo has no obs acles in he scena io. A e he sequen ial un o he nodes esponsible
o publishing he poses, he inal node se les he communica ion be ween he manipula o
in Mo eI and he one in CoppeliaSim, as p e iously explained.
As al eady exclaimed, he second launch ile handles he execu ion o he pick-and-
place ope a ions. Depending on he manipula ion scena io selec ed by he use , one o he
eigh possible ope a ions will be execu ed. So, his launch ile depends on he desi ed
ope a ion and akes he name o he CoppeliaSim model he a m mus pick o place as inpu .
Consequen ly, his launch ile is composed o a sequence o wo nodes, bo h o which ecei e
he launch ile's inpu as an a gumen . The i s one co esponds o a node ha eads he pose
o he CoppeliaSim model o be manipula ed, p o ided as an a gumen , and publishes i in
R iz. The second node execu es he planning code o he speci ied objec . By s uc u ing he
p ocess in his way, he scena io is always ead be o e p oceeding wi h he manipula ion
ope a ion. I he e is any posi ional a ia ion in he models in CoppeliaSim, Mo eI will upda e
his change, and he subsequen planning will ake his in o accoun . Following his logic, hese
codes could be easily adap ed o eal-wo ld applica ions. In he i s launch ile, came as would
de ec he eal- ime posi ions o he objec s ela i e o he a m depending on whe e he
pla o m s ops nea he amps o dollies. In he second launch ile, he came a would iden i y
110
success a e, pa h planning ime, and a pa h smoo hness me ic o alida e whe he he
ajec o y is smoo h. The la e me ic measu ed he angle be ween h ee consecu i e poin s,
whe e alues close o 0 indica e smoo he ajec o ies due o a highe a e o s aigh -line
segmen s. This s udy concluded ha he RRT-Connec planne is a good op ion o high-
complexi y scena ios.
Gi en his o e iew, i can be concluded ha selec ing he app op ia e mo ion planne
depends on he dis ibu ion o he manipula ion scena io. Consequen ly, a mo ion planning
benchma king s udy was conduc ed o he MIAR p ojec . The expe imen s we e ca ied ou
on a pe sonal compu e using Ubun u 22.04. The compu e consis ed o an MSI Ka ana 15
B13VGK-2040 lap op equipped wi h a 13 h-gene a ion In el Co e i7 p ocesso , 32 GB o RAM,
a 1 TB solid-s a e d i e (SSD), and an NVIDIA GeFo ce RTX 4070 GPU. I is no ewo hy ha he
compa ison was exclusi ely conduc ed using Mo eI , employing he pick-and-place codes
ou lined in sec ion 4.8.
A g oup o planne s was compa ed ac oss ou di e en scena ios co esponding o
he pick-and-place ope a ions o he wo ypes o boxes on he access amps. These scena ios
we e conside ed due o hei c i ical impo ance o he o e all p ojec and hei complexi y
ela ed o he limi ed space a ailable o placing he boxes on he amps. To ake bene i o
he bes planne , he wo s -case scena io was conside ed o each planning, whe e he obo ’s
wo kspace was ully occupied by he maximum possible numbe o objec s. Fo example,
when he manipula o needed o pick up o place 600x400 boxes on he amp, i was assumed
ha he pla o m was al eady ull o 400x300 boxes, and ice e sa.
The compa ison in ol ed he planne s RRT-Connec , T-RRT, BiEST, KPIECE, and
LazyPRM*, which we e highligh ed ea lie in he e iewed s udies. Op imized e sions o some
men ioned planne s, such as PRM* and RRT*, we e also included in he benchma king.
Addi ionally, planne s like Bi-TRRT, RRT, and P ojEST we e conside ed a e sa is ac o y esul s
we e ob ained du ing p elimina y es ing in he indica ed scena ios.
When i comes o choosing he benchma king me ics, he analysis conside ed o al
planning ime, o al execu ion ime, pa h leng h, and he success a e in inding a solu ion o
measu e he pe o mance o each planne . A smoo hness ac o was included o e alua e he
quali y o he gene a ed pa hs. This pa ame e is de i ed om he me ic used in he
benchma king s udy by Cohen e al. (2012) o measu e pa h smoo hness. Fo a pa h composed
o n segmen s, he angle α i be ween wo consecu i e segmen s is calcula ed, and he
111
ollowing Equa ion 5.1 is applied. The lowe he alue o his me ic, he smoo he he
ajec o y is conside ed.
𝐾=1𝑛 ∑𝛼𝑖2
𝑛
𝑖=2
5.1
In Mo eI , each planne includes mul iple pa ame e s ha can signi ican ly in luence
he pe o mance o he sampling-based planne s. Since modi ying and es ing each pa ame e
indi idually by planne would be a ime-consuming p ocess, all he men ioned planne s we e
compa ed using he de aul pa ame e s p o ided by he Mo eI 2 package. A planning ime o
1 second was speci ied o each planne , as he goal is o achie e as planning, along wi h he
cons ain s and mo ion kinema ics explained in Sec ion 4.8. Each planne was simula ed en
imes o each ope a ion. The op imiza ion-based planne CHOMP was ini ially conside ed o
his benchma king s udy. Howe e , his planne ypically gene a es long p ocessing imes, as
highligh ed in (S. Liu & Liu, 2022). Gi en he de ined cons ain s and he se led planning ime,
CHOMP was unable o ind a solu ion wi hou adjus men s o i s pa ame e s. As a esul , his
planne was excluded om he benchma king s udy.
The benchma king p ocess was inspi ed by he OMPL Planne A ena om Mo eI ,
u ilizing Tukey Boxplo s o compa e he pe o mance o each planne ac oss di e en me ics.
Simila o he Planne A ena, he plo analyses in his s udy exclude da a om ailed a emp s
by he planne s. This exclusion is c ucial o co ec ly in e p e ing he s udied plo s because
some planne s may p esen da a om he o al numbe o planning a emp s, while o he s
migh show a subse . To add ess his issue, as done in he Planne A ena, a able showing he
success a e o each planne is p esen ed alongside he plo s (Moll e al., 2015).
As he goal is o iden i y a sui able planne o all he equi ed ope a ions on he Bosch
shop loo , any planne s ha ail o compu e a solu ion wi hin he 10 de ined a emp s a e
au oma ically excluded om conside a ion.
The analysis o he ob ained esul s is ho oughly add essed in he subsequen sec ion.
112
5.2 Analysis o he Mo ion Planne s Compa ison
As explained in sec ion 5.1, a benchma king s udy o en OMPL planne s was pe o med
o he scena ios in ol ing he access amps, using he planning and execu ion imes, pa h
leng h, a smoo hness me ic, and he success a e in inding a solu ion as e alua ion me ics.
The esul s a e p esen ed below o he place ope a ion in ol ing he 600x400 boxes,
which consis s o placing he boxes on he uppe le el o he amp. Due o he many me ics
and planne s included in he compa ison, he analyses o he emaining ope a ions a e
p esen ed in Appendix F. In he ope a ion o placing he 600x400 boxes, i was obse ed ha
all he planne s p o ided ela i ely sho planning imes o bo h he placemen and e ea
pa hs (Figu e 80). Howe e , RRT-Connec and BiEST exhibi ed sligh ly highe alues compa ed
o he o he s.
Figu e 80 - Compa ison o planning and execu ion imes o he place ope a ion o he 600x400 boxes.
A signi ican disc epancy was obse ed be ween he planne s in e ms o execu ion
ime. The planne s ha demons a ed he bes esul s we e P ojEST, RRT, RRT*, PRM*, and T-
RRT. This la e planne con ained ou lie s, one in he place execu ion ime and wo in he
e ea execu ion ime. These ou lie s esul ed om execu ion imes ha exceeded he uppe
whiske , meaning alues highe han he uppe qua ile (Q3) by 1.5 imes he in e qua ile
ange. Al hough LazyPRM* and KPIECE had a high place and e ea execu ion imes, i is
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no able ha hal o hei alues a e concen a ed as hei median alues we e below 10
seconds.
These execu ion ime alues a e e lec ed in he pa h leng h o he en i e ope a ion
gene a ed by each planne (Figu e 81). Planne s wi h highe execu ion imes, such as BiEST
and RRT-Connec , p oduced longe pa hs, while planne s like RRT, P ojEST, and PRM* yielded
sho e pa hs.
Figu e 81 - Compa ison o he pa h leng h o he place ope a ion o he 600x400 boxes.
Using he me ic explained ea lie , smoo hness was obse ed. Planne s p oducing
longe pa hs ended o c ea e smoo he ajec o ies (Figu e 82). These planne s p io i ized
he mo ion cons ain s speci ied in he ope a ion code a he han inding he as es pa h o
he goal. As a esul , hey gene a ed longe and unnecessa y pa hs o yield mo e linea pa hs,
while o he planne s allowed la ge angles be ween he segmen s ha composed he pa h.
114
Figu e 82 - Compa ison o he smoo hness ac o o he place ope a ion o he 600x400 boxes.
Rega ding he success a e in inding a easible solu ion, mos planne s success ully
gene a ed a alid pa h, excep he RRT-Connec planne , which ailed in one a emp . Only
P ojEST, RRT, PRM*, and KPIECE consis en ly ound a solu ion on he i s a emp (Figu e 83).
Figu e 83 - Numbe o a emp s o he place ope a ion o he 600x400 boxes.
F om he pick ope a ion o he 600x400 boxes p esen ed in Appendix F, i is possible
o analyze ha only he Bi-TRRT and T-RRT planne s achie ed good esul s in e ms o planning
ime and execu ion ime o bo h he pick and e ea mo emen s o he ask, wi h Bi-TRRT
showing ou lie s o he pick execu ion ime. The emaining planne s exhibi ed high execu ion
ime alues o he pick mo emen , wi h e y dispe sed da a. These esul s a e also exp essed
in he pa h leng h me ic, as hese wo planne s gene a ed he sho es pa hs.
Rega ding he smoo hness ac o , he s andou planne s we e once again Bi-TRRT, T-
RRT, and RRT*. Unlike he p e ious ope a ion, all planne s success ully ound a pa h in his
ope a ion. Bi-TRRT, T-RRT, PRM*, and LazyPRM* ha e achie ed high success a es. Based on
his analysis, i can be concluded ha hese wo i s planne s we e he bes op ions o his
ope a ion.
115
Fo he place ope a ion wi h he 400x300 boxes, all he planne s gene ally p esen ed
good planning and execu ion imes, wi h he P ojEST, Bi-TRRT, and RRT planne s s anding ou .
Howe e , he RRT-Connec , LazyPRM*, and BiEST planne s showed high execu ion imes. The
planne s ha c ea ed he sho es pa hs we e Bi-TRRT, P ojEST, RRT, RRT*, and PRM*. Despi e
he a o able esul s p esen ed by he Bi-TRRT planne , i is impo an o no e ha i could
no ind a easible solu ion in all 10 a emp s. This planne ailed one ime o ind a solu ion
o he placing ope a ion and, consequen ly, o he e ea ing mo emen . RRT-Connec ,
BiEST, and LazyPRM* we e he planne s ha con ibu ed o smoo he ajec o ies. Howe e ,
once again, conside ing he success a e, he RRT-Connec and BiEST planne s ailed o ind a
solu ion a leas wice. The e o e, he RRT-Connec , Bi-TRRT, and BiEST planne s we e
excluded om he selec ion o he mos app op ia e planne o he MIAR p ojec , ega dless
o hei good pe o mance in o he ope a ions.
In he pick ope a ions wi h he 400x300 boxes, only wo planne s s ood ou in he
gene a ed imes: Bi-TRRT and T-RRT. While Bi-TRRT demons a ed sho e planning imes, T-
RRT p o ided sho e execu ion imes. Al hough his in e p e a ion migh sugges ha T-RRT
gene a ed sho e pa hs, when analyzing he plo based on he ope a ion leng h, i is e i ied
ha Bi-TRRT gene a ed sho e solu ions. This is con i med by i s lowe mean, smalle
in e qua ile ange, and sho e whiske s. Despi e being as e a gene a ing solu ions wi h
minimal dis ances, bo h Bi-TRRT, T-RRT, and KPIECE displayed ajec o ies wi h less
smoo hness. This is con i med by hei highe smoo hness ac o alues, which a e
app oxima ely 0.05. In con as , he RRT-Connec planne excelled in his me ic. When
examining he success a e, se e al planne s, namely BiEST, P ojEST, RRT, RRT*, and PRM*,
ailed o ind always a solu ion. O e 60% o he a emp s execu ed by P ojEST, RRT, and RRT*
we e unsuccess ul. Among all he planne s, Bi-TRRT was he only one ha consis en ly ound
a solu ion on he i s a emp .
The conduc ed benchma king s udy concluded ha many planne s could no p oduce
pa hs o he ope a ions in ol ing he manipula ion o he 400x300 boxes. This lowe success
a e compa ed o he asks in ol ing he 600x400 boxes can be a ibu ed o he limi ed space
be ween he pla o m and he access amps. The smalle boxes a e posi ioned a he base o
he pla o m, making he equi ed manipula o mo emen s mo e challenging han picking o
placing he la ge boxes in he concep ual s uc u e loca ed a he back o he KMR. Among
all he conside ed planne s only h ee we e able o ind sui able solu ions in all ou scena ios,
116
which we e KPIECE, LazyPRM* and T-RRT planne s. Since T-RRT deli e ed he bes o e all
esul s, pe o ming well ac oss all e alua ion me ics, i was chosen as he planne o he
MIAR p ojec .
5.3 Op imiza ion o he Mo ion Planne
T-RRT planne demons a ed sa is ac o y esul s o mos box manipula ion asks.
Howe e , as p esen ed in he p e ious analysis, i s pe o mance on he smoo hness me ic
was he wo s in he place ope a ion o 400x300 boxes, and i also showed high alues o
he pick ope a ion. One al e na i e o add ess his p oblem is u he limi ing he o ien a ion
cons ain o he manipula o 's end-e ec o . This adjus men would ensu e sa e handling o
he illed 400x300 boxes and educe he a iabili y in ajec o y gene a ion. The T-RRT planne
was cus omized by weaking i s pa ame e s o achie e as e solu ions wi hou ully
comp omising pa h quali y h ough an i e a i e p ocess. The ini ial empe a u e, pa ame e
ha was men ioned in Sec ion 3.2.4, was augmen ed as i is ecommended ha i should be
high a he beginning o he algo i hm o enable a b oade explo a ion (Ka aki Lab, 2024).
The max_s a es_ ailed pa ame e was educed o accele a e he empe a u e inc ease a e
a ew ailed ansi ions o new s a es, while he emp_change_ ac o was aised o p omo e
as e empe a u e adap a ions du ing ailed ansi ion es s. I is impo an o emphasize ha
while hese changes may inc ease he sea ch o solu ions, hey could lead o poo e pa hs
being ound. On he o he hand, o ensu e sa e handling and educe il ing du ing
manipula ion, he o ien a ion cons ain o he end-e ec o was es ic ed o he 400x300
boxes. This cons ain was also adjus ed o he placemen code o he 600x400 boxes, as hey
a e placed ull on he uppe le el o he amp. Mo eI includes pos -p ocessing algo i hms o
ime pa ame e iza ion kinema ic ajec o ies, conside ing he eloci y and accele a ion
alues. To p e en je ky mo emen s o he manipula o and imp o e smoo hness, he Ruckig
je k-limi ed smoo hing algo i hm was used du ing he pick-and-place ope a ions (PickNik
Robo ics, 2024d). The pe o mance compa ison be ween his cus om T-RRT and he de aul
one o he benchma king me ic ac oss he di e en ope a ions is depic ed in Appendix G.
Ano he pos -p ocessing op imiza ion echnique ha can be employed is using CHOMP
as a pos -p ocesso o OMPL (PickNik Robo ics, 2024e). In his app oach, he cus om T-RRT
inds a solu ion, and CHOMP subsequen ly op imizes he ajec o y. The CHOMP ajec o y
117
ini ializa ion me hod illT ajec o y was selec ed o ensu e ha he compu ed pa h om T-RRT
was ecei ed. Simila ly o he p e iously conside ed p ocess, he CHOMP pa ame e s we e
modi ied i e a i ely o gua an ee a solu ion in he sho es possible ime. The maximum
numbe o i e a ions a e es ablishing a collision- ee ajec o y was educed, he weigh o
smoo hness in he cos unc ion was conside ed, a minimum obs acle clea ance was de ined,
and he enable_ ailu e_ eco e y pa ame e was se o ue, which enables CHOMP o adjus
i s pa ame e s in case he i s a emp wi h he speci ied pa ame e s ails. The pe o mance
o his pa ame e is also illus a ed in Appendix G.
Fo ope a ions in ol ing he 400x300 boxes, i was obse ed ha he cus om T-RRT
could gene a e as e pa hs, e en hough he manipula o was mo e es ic ed. The execu ion
ime alues we e simila o he de aul planne , bu he pa h leng h was sho e wi h mo e
concen a ed alues, as indica ed by he smalle in e qua ile ange. This educed a ia ion in
alues may be a ibu ed o es ic ions imposed in he codes ha o ce he algo i hm o
execu e ajec o ies in a ce ain di ec ion consis en ly. In bo h ope a ions, he use o es ic ed
o ien a ion cons ain s con ibu ed o smoo he pa hs, pa icula ly in he placemen scena io,
whe e he educ ion was signi ican . Rega ding he T-RRT wi h CHOMP, i was e i ied ha
al hough he OMPL quickly ound ini ial solu ions and he CHOMP pa ame e s we e adjus ed,
he pos -p ocessing ime emained leng hy. The planning ime anged om 6 o 7 seconds,
which is oo long o p ac ical eal-wo ld applica ions. Fo he smoo hness me ic, his planne
achie ed low alues and, in he pick ope a ion, e en ou pe o med he cus om T-RRT.
Al hough no included in Appendix G, in he en simula ions conduc ed o each planne , bo h
we e able o ind solu ions, usually in one o wo a emp s. In one simula ion o he pick
ope a ion, he planne T-RRT wi h CHOMP equi ed six a emp s o ind a solu ion o he
e ea mo emen o he home posi ion. This esul was e lec ed in he ou lie in he planning
ime o he e ea mo emen in he espec i e ope a ion.
Rega ding he pick and place ope a ions in ol ing he la ge boxes, he cus om T-RRT
planne gene ally demons a ed sho e planning imes han he de aul planne . Howe e ,
i s execu ion imes we e sligh ly highe in bo h ope a ions. In u n, he de aul planne
exhibi ed highe mean execu ion imes o he place ope a ion due o he p esence o ou lie s.
The cus om planne p oduced sho e ajec o ies o he pa h leng h me ic in bo h
ope a ions. Conce ning he smoo hness me ic, bo h planne s displayed simila alues o he
pick ope a ion, as he e ea phase consis s o a sho mo emen wi hou any collision objec s
118
in i s pa h. None heless, cus om T-RRT had be e esul s in he place ope a ion. As p e iously
discussed, his pe o mance beha io may esul in he es ic ed o ien a ion cons ain
applied o his ope a ion. The cus om T-RRT wi h CHOMP planne accomplished esul s simila
o hose o he cus om T-RTT. Ne e heless, i equi ed longe planning imes due o he pos -
p ocessing s ep, esul ing in alues o a ound 6 o 7 seconds.
F om all his analysis, i can be concluded ha bo h he cus omized T-RRT planne and
he planne in conjunc ion wi h CHOMP deli e ed be e esul s in he smoo hness me ic o
small box ope a ions. This ou come was desi ed, as he de aul T-RRT planne exhibi ed high
alues o his me ic. The planne s had simila esul s o ope a ions wi h la ge boxes,
al hough he wo cus omized planne s gene a ed sho e pa hs han he de aul one. I is also
e iden ha adding CHOMP as a pos -p ocesso did no signi ican ly enhance he pe o mance
o he cus om T-RRT. The esul s emained simila , wi h he addi ional d awback o inc eased
planning ime. This is likely a ibu ed o he pa ame e adjus men s made o CHOMP, whe e
he conce n was minimizing he pos -p ocessing ime a he han imp o ing he planne 's
smoo hness. The e o e, based on he ealized s udy, he cus omized T-RRT is he mos sui able
planne o he wo king en i onmen p esen in he MIAR p ojec .
5.4 Manipula ion Ope a ions Using he Selec ed Mo ion Planne
The cus omized T-RRT mo ion planne demons a ed he bes pe o mance, acco ding
o he s udies conduc ed ea lie . The compa ison ocused solely on scena ios whe e he boxes
we e s o ed on he access amps due o he challenging na u e o his en i onmen o he
manipula o du ing he asks. Howe e , his e alua ion did no include he ou addi ional
scena ios whe e he obo picks and deposi s he Ta ge s in he dollies loca ed a he Dolly
Supply a ea. The e o e, he chosen mo ion planne was es ed o he eigh manipula ion
scena ios o ensu e i s sui abili y o he MIAR p ojec . This analysis conside ed all possible
pick-and-place ope a ions in ol ing he anspo o he Ta ge s. Unlike he p e ious
benchma king s udies, hese es s inco po a ed eal- ime communica ion be ween Mo eI
and CoppeliaSim.
This analysis e i ied ha he planning imes occasionally exceeded expec a ions
compa ed o he esul s ob ained solely in Mo eI . This sligh disc epancy can be a ibu ed
o he con inuous communica ion be ween he wo so wa e sys ems, which imposes g ea e
119
compu a ional demands on he sys em. Despi e his, he planne success ully iden i ied
easible solu ions o he a ious case scena ios.
The chosen planne was de e mined o e ec i ely accomplish all in ended asks wi h
sa is ac o y esul s. Figu e 84 shows he ou comes o he picking ope a ions o he 600x400
boxes and 400x300 boxes om he amp.
(a)
(b)
Figu e 84 - (a) Picking 600x400 boxes om he amp. The ask can be seen in: h ps://you u.be/4_d 845m8Tw; (b) Picking
400x300 boxes om he amp. The ask can be seen in: h ps://you u.be/8CKV2Hu8QAo.
Simila ly, he placemen o he 600x400 boxes on he amp, as well as he placemen
o he 400x300 boxes, can be checked in Figu e 85.
(a)
(b)
Figu e 85 - (a) Placing 600x400 boxes in he amp. The ask can be seen in: h ps://you u.be/a5ITRRm8M_8; (b) Placing
400x300 boxes in he amp. The ask can be seen in: h ps://you u.be/GSF92bFSyIc.
126
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