elec onics
A icle
Scan Ma ching by C oss-Co ela ion and
Di e en ial E olu ion
Ja omi Konecny 1,* , Pa el K ome 1, Michal P auzek1and Pe Musilek2
1Facul y o Elec ical Enginee ing and Compu e Science, VSB—Technical Uni e si y o Os a a,
708 00 Os a a, Czech Republic
2Depa men o Elec ical and Compu e Enginee ing, Uni e si y o Albe a,
Edmon on, AB T6G 1H9, Canada
*Co espondence: ja omi [email p o ec ed]; Tel.: +420-59-732-5996
Recei ed: 28 May 2019; Accep ed: 30 July 2019; Published: 1 Augus 2019

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Abs ac :
Scan ma ching is an impo an ask, sol ed in he con ex o many high-le el p oblems
including pose es ima ion, indoo localiza ion, simul aneous localiza ion and mapping and o he s.
Me hods ha a e accu a e and adap i e and a he same ime compu a ionally e icien a e equi ed
o enable loca ion-based se ices in au onomous mobile de ices. Such de ices usually ha e a
wide ange o high- esolu ion senso s bu only a limi ed p ocessing powe and cons ained ene gy
supply. This wo k in oduces a no el high-le el scan ma ching s a egy ha uses a combina ion
o wo ad anced algo i hms ecen ly used in his ield: c oss-co ela ion and di e en ial e olu ion.
The c oss-co ela ion be ween wo lase ange scans is used as an e icien measu e o scan alignmen
and he di e en ial e olu ion algo i hm is used o sea ch o he pa ame e s o a ans o ma ion ha
aligns he scans. The p oposed me hod was expe imen ally alida ed and showed good abili y o
ma ch lase ange scans aken sho ly a e each o he and an excellen abili y o ma ch lase ange
scans aken wi h longe ime in e als be ween hem.
Keywo ds: scan ma ching; indoo localiza ion; di e en ial e olu ion; c oss-co ela ion; obo ics
1. In oduc ion
The de e mina ion o he posi ion o a mo ing objec is an essen ial pa o many complex
applica ions. While ou doo localiza ion can be achie ed wi h he help o global sa elli e ne wo ks
including he Global Posi ioning Sys em (GPS) and he Global Na iga ion Sa elli e Sys em (GLONASS),
an e icien indoo localiza ion is s ill an open p oblem [
1
,
2
]. I can be de ined as he p ocess o
ob aining he loca ion o a mo ing objec in an indoo en i onmen [
2
]. Indoo localiza ion is an
enabling echnology o a a ie y o loca ion-based se ices ha can be used in he con ex o ad anced
manu ac u ing (Indus y 4.0) [
3
], In e ne o hings [
2
], sma buildings [
1
], indoo (unde g ound)
escue ope a ions [4,5] and many o he applica ions.
Sel -localiza ion o an au onomous mobile obo o an unmanned ae ial ehicle (UAV) [
6
], a special
ype o indoo localiza ion, is one o he g ea challenges o mode n obo ics [
7
,
8
]. I elies on an
independen measu emen and analysis o senso da a ha pe o med by he obo o es ima e i s own
posi ion and mo ion ajec o y in an unknown indoo en i onmen . In con as o o he ypes o indoo
localiza ion, i does no use any ex e nal signals, beacons o o he in o ma ion han is no sensed by
he obo i sel [
8
]. Sel -localiza ion is associa ed wi h he p oblem o simul aneous localiza ion and
mapping (SLAM). As SLAM, i equi es app oaches ha a e accu a e, obus and compu a ionally
e icien a he same ime [8].
The e a e many me hods o mobile obo indoo sel -localiza ion [
2
,
7
,
9
–
11
]. In gene al, hey a e
based on ideo signals analysis and compu e ision, in a ed and ul asound senso s, lase ange
Elec onics 2019,8, 856; doi:10.3390/elec onics8080856 www.mdpi.com/jou nal/elec onics
Elec onics 2019,8, 856 2 o 20
inde s, sona sys ems [
7
,
12
], adio- equency iden i ica ion (RFID), wi eless ne wo k echnologies
such as Wi-Fi, Blue oo h [
10
,
11
] and Zigbee [
2
], ul a-wideband (UWB), magne ic senso s and acous ic
signal analysis [
2
,
10
]. Indoo sel -localiza ion by ligh de ec ion and anging (LiDAR) elies on analysis
o a sequence o lase ange scans. The scans cap u e he su oundings o he obo as a se ies o poin s
ep esen ing he in e sec ions o he lase beam wi h nea by objec s [
7
]. They gene a e sequences o 2-
o 3-dimensional poin clouds ha a e mu ually compa ed (ma ched) o app oxima e he ajec o y
o he obo in he en i onmen . In gene al, scan ma ching algo i hms can be spli in o wo majo
g oups. Poin -based app oaches p ocess he en i e poin clouds, while ea u e-based echniques ocus
on ea u es ex ac ed om he poin clouds by a ious ea u e ex ac ion algo i hms. The ea u es a e
seen as landma ks and he changes in hei ( ela i e) loca ions a e used o es ima e he mo es o he
obo [7].
Ad anced me hods ha u ilize a i icial in elligence, machine lea ning and so compu ing can be
used o di e en ypes o sel -localiza ion applica ions. Fo example, a i icial neu al ne wo ks and
suppo ec o machines ha e been used o build indoo localiza ion models based on he ecei ed
signal s eng h indica o (RSSI) [
2
]. In his wo k, a no el scan ma ching algo i hm based on di e en ial
e olu ion and modi ied c oss-co ela ion is in oduced. C oss-co ela ion is used o e alua e he
alignmen o lase ange scans, while di e en ial e olu ion se es as an op imiza ion me hod o he
app oxima ion o he scan ma ching pa ame e s.
The con ibu ions o his wo k a e wo old: (1) I shows ha he di e en ial e olu ion can be
used as an op imiza ion mechanism in a poin -based scan ma ching s a egy; and (2) I demons a es
ha c oss-co ela ion is a compu a ionally e icien and a he same ime obus poin cloud alignmen
measu e. The ex ensi e expe imen al e alua ion o hese no el concep s also demons a es ha he
scan ma ching p ocedu e based on di e en ial e olu ion and c oss-co ela ion can be used o accu a e
indoo localiza ion o au onomous mobile de ices.
The emainde o his a icle is s uc u ed in he ollowing way. The p oblem o localiza ion
is summa ized and ela ed wo k is e iewed in Sec ion 2. The algo i hms used in his wo k
(scan ma ching, c oss-co ela ion and di e en ial e olu ion) a e desc ibed in Sec ion 3. The p oposed
app oach is de ailed in Sec ion 4and expe imen ally e alua ed in Sec ion 5. The esul s o conduc ed
expe imen s a e discussed in Sec ion 6and he a icle is concluded in Sec ion 7which also ou lines
u u e esea ch di ec ions.
2. Rela ed Wo k
Al hough indoo localiza ion has been add essed by a ple ho a o me hods and algo i hms wi h
a ious p ope ies, i s ill emains an open p oblem. Tigh ly linked o mapping o (unknown) indoo
en i onmen s, i is an essen ial elemen o he compound p oblem o simul aneous localiza ion and
mapping (SLAM) [
13
,
14
]. Di e en ypes o localiza ion and SLAM algo i hms ha e been de eloped
o a ious ypes o en i onmen s [
15
]. Accu a e SLAM algo i hms ha e been p oposed o la ge
ou doo a eas [
16
] and limi ed indoo spaces [
17
]. Mon e Ca lo localiza ion (MCL) is a popula amily
o localiza ion me hods [
9
,
18
,
19
] ha use, among o he s, pa icle and Kalman il e s [
20
]. A he
s a ing poin o he MCL p ocess, a pool o andom posi ions and angles is c ea ed. When he obo
mo es h ough an en i onmen , he algo i hm upda es all posi ions in he pool acco ding o a obo
mo ion model. The expec ed obo su ounding is compa ed o da a om a senso (e.g., he LiDAR)
su eying he ac ual en i onmen and he posi ions ha co espond o he eal da a mos a e ewa ded.
The disad an age o he MCL me hod is he necessi y o obo mo emen and he need o addi ional
senso s (e.g., odome e s) ha a e equi ed by he mo ion model [21].
Ano he amily o p omising SLAM app oaches is based on he use o e en came as [
22
].
E en came as p oduce sequences o ideo ames and, addi ionally, in o ma ion abou b igh ness
changes on he pixel le el. The ad an ages o e en came as include e y high dynamic ange,
absence o mo ion blu and only a small la ency (in he o de o mic oseconds [
23
]). An o e iew o
SLAM algo i hms ha use e en came as is p o ided, o example, in [24].
Elec onics 2019,8, 856 3 o 20
Localiza ion is also one o he majo challenges o UAVs. They equi e in o ma ion abou p ecise
loca ion in o o de o a oid obs acles [
25
] and o ajec o y planning [
26
]. UAVs can, in gene al,
implemen simila localiza ion app oaches as mobile obo s. Howe e , he localiza ion me hods need
o be adjus ed o add ess he speci ics o ae ial mo emen such as 3D SLAM. A comp ehensi e e iew
o localiza ion s a egies o UAVs can be ound in [6].
Scan ma ching [
27
,
28
] is a g oup o popula high-le el localiza ion/SLAM me hods ha p ocess
lase ange scans o an en i onmen [
29
]. They align wo lase ange scans o he (usually unknown)
en i onmen in o de o de ec he change o he loca ion and o ien a ion o a mo ing objec [
30
].
Scan ma ching algo i hms can be classi ied as poin -based and ea u e-based. Poin -based me hods
p ocess lase ange scans poin -by-poin whe eas ea u e-base me hods ex ac highe -le el ea u es
such as lines, co ne s and so o h, and align hese ea u es. Fea u e-based me hods ex ac dis inc i e
ea u es be o e ma ching i sel and hus dec ease he amoun o da a ha needs o be p ocessed. As a
esul , hei scan ma ching phase has lowe compu a ional cos s bu hey su e om lowe obus ness
and wo se accu acy in ich and well-s uc u ed en i onmen s.
I e a i e closes poin (ICP) is a ypical ep esen a i e o poin -based scan ma ching algo i hms [
31
].
ICP is a seminal me hod ha has a numbe o modi ica ions [
32
,
33
]. A ep esen a i e o ea u e-based
scan ma ching s a egies is he comple e line segmen (CLS) me hod [
34
]. I looks o la a eas in poin
clouds, ex ac s lines and de ec s comple e and incomple e line segmen s. I expec s ha a comple e line
segmen in an en i onmen has a speci ic cons an leng h om any poin o iew. O he ea u e-based
scan ma ching s a egies include he ancho poin ela ionships (APR) algo i hm [
35
] ha de ec s
speci ic ancho s, plane ex ac ion app oaches [36] and keypoin and keyline ex ac ion [37].
Na u e-inspi ed me hods, such as e olu iona y compu a ion, ha e been used in he a ea o mobile
obo localiza ion as well. In [
38
], he di e en ial e olu ion algo i hm was used in conjunc ion wi h
he adi ional no mal dis ibu ion ans o m (NDT) algo i hm [
39
]. Ano he wo k used di e en ial
e olu ion as pa o a ea u e-based scan ma ching algo i hm ha ex ac ed lines, planes and sphe es
om lase ange scans [
40
]. O he na u e-inspi ed me hods such as he ha monic sea ch algo i hm
we e used o di e en ial scan ma ching as well [41].
This wo k p oposes a no el scan ma ching algo i hm based on a combina ion o wo ecen ly
in oduced app oaches. The c oss-co ela ion app oach [
42
,
43
] is adop ed o he assessmen o lase
ange scans’ simila i y and he di e en ial e olu ion is used o he sea ch o accu a e lase ange scan
ans o ma ion pa ame e s [
44
]. The e alua ion o he p oposed scan ma ching s a egy is pe o med
in a se ies o simula ion expe imen s wi h he help o a so wa e amewo k in oduced in [45].
3. Backg ound
This sec ion p o ides he backg ound o he p esen ed wo k. I ou lines he simula ion-based
design s a egy i adop s, ele an scan ma ching me hods such as he i e a i e closes poin algo i hm,
he undamen als o he c oss-co ela ion p inciple and he op imiza ion p ocess implemen ed by he
di e en ial e olu ion.
3.1. Expe imen al Se up and Embedded Da a P ocessing
The aim o his wo k is he design o a localiza ion algo i hm sui able o an au onomous
mobile ehicle, o example a wheeled mini obo o explo a ion, su eillance and escue ope a ions.
Ha dwa e a chi ec u e o such ehicle was desc ibed, o example, in [
46
]. The mechanical cons uc ion
o he ehicle was based on he RC Baja 5B SS chassis and i was equipped wi h all necessa y elec onic
de ices ha allowed he con ol o i s mo emen . The ehicle was also equipped wi h he SICK LMS
100 LiDAR and a se o odome y senso s.
A no el algo i hm o a speci ic sys em o de ice ough o be alida ed in e ms o co ec ness,
accu acy, eliabili y and obus ness. In o de o allow apid p o o yping and e alua ion o a ious
app oaches, a model-based de elopmen using a so wa e simula ion o pa icula sys em componen s
(i.e., So wa e in he Loop) was adop ed o alida e he scan ma ching algo i hm. The simula ion
Elec onics 2019,8, 856 4 o 20
amewo k p o ides in o ma ion abou he ue posi ion and o ien a ion o he de ice, simula es i s
mo emen in a p e-de ined indoo en i onmen and p oduces simula ed LiDAR and odome y da a.
The s uc u e o he en i onmen is de ined by a loo plan. The a ge p ocesso is an Ad anced
RISC Machine (ARM) Co ex-M mic ocon olle expec ed o un he scan ma ching algo i hm and o
compu e he es ima ed posi ion and o ien a ion o he de ice in he eal de ice. This op–le el design
s a egy is isually illus a ed in Figu e 1.
Figu e 1. An ou line o he simula ion-based design.
An ARM Co ex-M p ocesso suppo s di e en unc ionali y depending on i s e sion. Table 1
desc ibes he basic ea u es o se e al ecen ARM Co ex-M e sions (M0+, M3, M4 and M7) [
47
].
In gene al, he p oposed app oach makes use o summa ion, mul iplica ion and di ision ope a ions
ha can be implemen ed as in ege o loa ing-poin ope a ions.
Elec onics 2019,8, 856 5 o 20
Table 1. O e iew o a ious ARM Co ex-M ea u es use ul o compu a ional localiza ion.
ARM Co ex-M Ve sion M0+ M3 M4 M7
A chi ec u e CPU a chi ec u e Von Neumann Ha a d Ha a d Ha a d
Pipeline s ages 2 3 3 6
In ege ope a ions
MULT 32 bi Fas /Slow Fas Fas Fas
DIV 32 bi No Yes Yes Yes
DSP No No Yes Yes
Floa ing-poin ope a ions FPU single p ecision No No Op ional Op ional
FPU double p ecision No No No Op ional
The pe o mance o a p ocesso can be assessed om h ee di e en pe spec i es. An ARM
Co ex-M p ocesso can implemen he on Neumann o he Ha a d a chi ec u e. The Ha a d
a chi ec u e has a sepa a e ins uc ion bus connec ed o an in e nal c oss-ba bus. I suppo s ha dwa e
pa allelism by allowing simul aneous access o ins uc ions and da a. The second impo an p ope y
o he implemen ed a chi ec u e is he numbe o s ages in he ins uc ion pipeline. A highe numbe
o pipeline s ages can accele a e ins uc ion execu ion and inc ease he compu a ional powe o
a p ocesso . Fo in ege ope a ions, he p ocesso implemen s an add ins uc ion as a s anda d
unc ionali y o an a i hme ic logic uni (ALU). Howe e , mul iply, di ide and digi al signal p ocessing
(DSP) ins uc ions a e op ional. ARM Co ex-M amily p ocesso s can be equipped wi h slow
(32 cycles) o as (1 cycle) mul iply ins uc ions, 32-bi di ide ins uc ions and digi al signal p ocessing
ins uc ions (e.g., a mul iply–accumula e ope a ion) use ul o inpu signal il e ing. I he execu ed
algo i hm uses loa ing-poin da a ypes, hen he p esence o a loa ing-poin uni (FPU) is highly
ecommended due o he long p ocessing imes wi hou his ma hema ical co-p ocesso . An FPU
can be ealized in he p ocesso co e as a single (32-bi ) o a double (64-bi ) p ecision e sion o a
ma hema ical co-p ocesso .
The selec ion o a sui able p ocesso co e e sion depends no only on da a- ype implemen a ion
bu he e a e se e al impo an algo i hm pa ame e s including he esolu ion o inpu da a, g id map
cell size and he ype and con igu a ion o he op imiza ion p ocedu e.
3.2. Scan Ma ching
Scan ma ching is a high-le el sel -localiza ion s a egy based on he assump ion ha wo
spa io- empo ally colloca ed lase ange scans o an en i onmen a e alike and can be ( o a la ge
ex en ) aligned [
48
]. Scan ma ching me hods seek ans o ma ions ha align wo lase ange scans
aken by a obo in he same en i onmen bu a di e en loca ions and om a di e en angle. The i s
lase ange scan, aken a he i s loca ion, is usually called he e e ence scan and he second lase
ange scan, aken a he second loca ion, is called he cu en scan. The ans o ma ion ha aligns he
scans is de ined by pa ame e s ha desc ibe he ela i e posi ion and o a ion o he scan (see Figu e 2).
Figu e 2a shows wo lase ange scans be o e he ans o ma ion (alignmen ) and Figu e 2b shows he
same scans a e a success ul alignmen .
Scan ma ching is mos o en based on 2 o 3-dimensional poin clouds cap u ed by LiDAR lase
ange inde s. The LiDAR pe iodically measu es he dis ance o he nea es objec in he di ec ion
o a lase beam i emi s [
48
]. In a 2-dimensional LiDAR, he measu ing lase beam is o a ed on he
ho izon al plane and c ea es a lase ange scan ha co esponds o he su ounding o he scanne [
49
].
3-dimensional LiDARs also il he measu ing senso in he e ical di ec ion and ob ain 3-dimensional
poin clouds [
50
]. A ypical 2-dimensional LiDAR lase ange inde , also used in his s udy, is Sick
LMS 100 by SICK AG. This ype o ange scanne p oduces coun e clockwise o ien ed ec o s o
dis ances o he nea es obs acle. The ou pu o he scanne is a ange ec o ,
~
a=h|a1|,|a2|, . . . , |asmax |i, (1)

Elec onics 2019,8, 856 6 o 20
composed o a sequence o dis ances o he nea es objec s,
|a1|
,
|a2|
,
. . .
,
|asmax |
and
smax
is he
numbe o measu emen s eps wi hin he ape u e ange o he scanne . Each measu ed dis ance,
|aφi|
,
co esponds o a pa icula angle, φiand each ange ec o ,~
a, co esponds o a ec o o angles,
~
φ=hφ1,φ2, . . . , φsmax i, (2)
whe e he index o he angle co esponds o he o ien a ion o he lase beam. The ange ec o ,
~
a
,
oge he wi h he angle ec o ,
~
φ
, desc ibe he su ounding o he scanne in he pola coo dina e
sys em. The lase ange scan, (~
a,~
φ), can be ans o med o he Ca esian coo dina es by
A= h|a1| · cos(φ1),|a2| · cos(φ2), . . . , |asmax | · cos(φsmax )i
h|a1| · sin(φ1),|a2| · sin(φ2), . . . , |asmax | · sin(φsmax )i!, (3)
whe e
A∈R2×smax
is a eal ma ix wi h he i s ow ep esen ing he
x
coo dina es and he second
ow o he
y
coo dina es o he poin s in he scan exp essed in Ca esian coo dina es. Each column o
A,~
as∈A, co esponds o a single poin o he scan in Ca esian coo dina es:
~
as= ax
ay!= |as| · cos(φs)
|as| · sin(φs)!,s∈ {1, smax}(4)
The scan ma ching p oblem can be o mula ed as he sea ch o a ec o o pa ame e s,
~
=h x, y,Φi, o an a ine ans o ma ion,
T(~
as, x, y,Φ) = cos Φ−sin Φ
sin Φcos Φ!·~
as+ x
y!,∀s∈ {1, smax}, (5)
ha leads o he bes alignmen o he e e ence scan o he ans o med cu en scan.
(a) (b)
Figu e 2. Scan ma ching: p oblem de ini ion. (a) Scans be o e alignmen (b) Scans a e alignmen .
Elec onics 2019,8, 856 7 o 20
3.3. I e a i e Closes Poin
The I e a i e closes poin algo i hm is he de- ac o s anda d poin -based scan ma ching algo i hm.
I is based on he sea ch o he pai s o he closes poin s in he ma ched lase ange scans [
51
]. Fo each
poin in he aligned scan, i inds he nea es poin in he e e ence scan and seeks ans o ma ion
pa ame e s ha minimize he Euclidean dis ance be ween hese wo poin s [
31
]. The ICP consis s o
he ollowing s eps [51]:
1. P ep ocessing
2. Ma ching
3. Rejec ion
4. Cos unc ion e alua ion
5. Minimiza ion o he cos unc ion (go o s ep 1. when e mina ion c i e ia a e no me )
In he p ep ocessing s ep, he poin s ha a e no use ul o ma ching o he wo poin clouds
(e.g., ou lie s) a e il e ed ou o educe he olume o he da a. The pai s o he closes poin s in he
ma ched scans a e ound in he ma ching phase. The ejec ion phase disca ds he poin pai s wi h oo
la ge dis ance in-be ween.
The cos unc ion,
cos
, ha e alua es he le el o alignmen be ween he e e ence scan,
A
and he
cu en scan, B, is de ined as [52]
cos A,B, x, y,Φ=
smax
∑
s=1

T(~
as, x, y,Φ)−~
bϑ(s)


2, (6)
whe e
T
is an a ine ans o ma ion de ined in Equa ion (5),
ϑ
ep esen s he unc ion ha inds o
each poin
~
as∈A
he nea es poin
~
bϑ(s)∈B
. The pa ame e s o
T
in ICP a e ound by an a bi a y
eal-pa ame e op imiza ion me hod, o example he New on-Raphson me hod [53].
3.4. C oss-Co ela ion
C oss-co ela ion is a concep known in he a ea o signal p ocessing. I is a measu e ha
e alua es he simila i y be ween wo signals,
x
and
y
, shi ed in ime by a speci ic alue,
τ
[
54
].
The c oss-co ela ion o wo a bi a y signals, exp essed by Ndisc e e samples,
Rxy(τ) =
N−1
∑
i=0
xi( )·yi( −τ), (7)
eaches maximum o a alue o
τ
o which a e he signals mos simila . In his s udy,
he c oss-co ela ion p inciple is used o ma ch wo lase ange scans o indoo obo localiza ion.
C oss-co ela ion o a lase ange scan,
A
, wi h a ansla ed and o a ed e sion o ano he scan,
B
,
is maximized when he pa ame e s o he ans o ma ion ha co espond o he cumula i e ansi ion
and o a ion o he obo (scanne ) be ween he scans we e aken a e ound [
42
]. The e alua ion o he
c oss-co ela ion be ween wo 2-dimensional lase ange scans unde a ine ans o ma ion
T
wi h
pa ame e ec o ~
= ( x, y,Φ)can be exp essed by
RAB( x, y,Φ) = A(T(B, x, y,Φ)), (8)
whe e

is an ope a o ha compa es wo 2-dimensional lase ange scans and quan i ies he deg ee o
hei alignmen (i.e., an implemen a ion o Equa ion (7) sui able o he compa ison o 2-dimensional
signals). The de ini ion o

is essen ial o he p ope ies o he p ocess. A simple measu e such as
he oo mean squa e e o (RMSE) can p o ide a easonable es ima e o he deg ee o scan alignmen
and i can be used as a pa o an op imiza ion-based scan ma ching p ocedu e [
44
]. Howe e ,
i s compu a ional complexi y is oo high o p ac ical use. In his wo k, an e icien nume ical algo i hm,
Elec onics 2019,8, 856 8 o 20
implemen ing he c oss-co ela ion p inciple o 2-dimensional signals, is used ins ead o RMSE o
e alua e he le el o alignmen o wo lase ange scans in he scan ma ching p ocedu e.
In he p oposed app oach, he lase ange scan is con e ed o Ca esian coo dina es in he same
manne as in [
44
]. Nex , a g id map simpli ying he scene is c ea ed om he poin cloud da a. The g id
map can be build using an a bi a y compu a ionally easible p ocedu e. Figu e 3illus a es wo
me hods o g id map c ea ion. The app oach, shown in Figu e 3a, is based on a ea compa ison.
I assumes ha he bes scan ma ch is achie ed when he o al olume o he o e lapping egions
is maximized. Fo each cell in he g id, he algo i hm decides whe he i is inside o he i s o he
second scan and hen compu es he numbe o o e lapping cells. The second me hod, shown in
Figu e 3b, is based on bounda y line analysis. I assumes ha he bes scan ma ch is ob ained when
he in e sec ion o he bounda y lines is maximized. This app oach does no equi e any ope a ions
o e emp y g id cells and lase scans can be ep esen ed by lis s o non-emp y g id cells ha con ain
he poin s o he scans.
(a) (b)
Scan B
Scan A In e sec ion
Figu e 3. Deg ee o alignmen app oaches: (a) A ea compa ison (b) Bounda y line compa ison.
Du ing he g id map c ea ion, mo e han one poin can be loca ed in a single g id cell. This ac
can be used by he scan ma ching p ocedu e. Fo example, each cell can ha e a weigh co esponding
o he numbe o poin s i con ains [
42
]. The cell weigh can hen a ec he emainde o he scan
ma ching p ocedu e. Howe e , ini ial expe imen s ca ied ou in he scope o his s udy showed ha
he use o cell weigh s leads o he p ema u e con e gence o he op imiza ion p ocess and, in many
cases, i p e en s he algo i hm om eaching he global op ima. The scan ma ching algo i hm is
mo e obus when he cell weigh s a e no aken in o accoun and he g id cells a e simply ma ked as
occupied o emp y. The numbe o occupied cells is usually no g ea e han 10% o all g id cells and
he c ea ion o g id maps as well as hei compa ison is as .
3.5. Di e en ial E olu ion
Di e en ial e olu ion (DE) is a success ul s ochas ic e olu iona y op imiza ion me hod o
con inuous pa ame e op imiza ion [
55
,
56
]. I is an e olu iona y op imiza ion p ocess based on
he concep o scaled ec o di e en ials. The DE ep esen s a con inuous al e na i e o he widesp ead
gene ic algo i hms ha wo k wi h a disc e e encoding o he candida e solu ions. Bo h algo i hms a e
na u e-inspi ed p oblem-sol ing s a egies ha e ol e a popula ion o candida e solu ions. On he
o he hand, hey use di e en solu ion encodings ( eal– alued s. disc e e one), apply di e en
ope a ions o e ol e he popula ion and as a esul implemen di e en sea ch s a egies.
Elec onics 2019,8, 856 9 o 20
The DE algo i hm has a his o y o success ul applica ions in many indus ial and enginee ing
domains. I was designed as a gene ic global op imiza ion me aheu is ic bu wi h p ac ical enginee ing
applica ions in mind [
56
]. I was used, among o he s, o p edic he g ound s a e s uc u es o
hyd ogena ed amo phous silicon (Si-H) clus e s in ma e ial science, o s eamline non-imaging op ical
design in op ics and ligh ning de elopmen , o achie e 3D image egis a ion in heal hca e imaging,
o design ans e sal digi al il e s in elec onics and in pa icula signal p ocessing, o use senso
da a in obo ics , o op imize indus ial comp esso supply sys ems, o ealize sys em iden i ica ion
o decision making and in gene al in he a ea o obo ics and expe sys ems [
56
]. The algo i hm
has also been applied in elec ical enginee ing and elec omagne ics. Fo example, i was used o
op imize design o an ennas o low signal- o-noise a io condi ions, o imp o e powe alloca ion
o he in e lea e-di ision mul iple-access channel access me hod, o op imize an enna loca ions
in a wi eless ne wo k o maximum space co e age and o op imize sou ce pulses and de ec ion
empla e in ul a-wideband adio sys ems. In he a ea o elec omagne ics, he DE has been used o
sol e elec omagne ic in e se sca e ing p oblems, he equency assignmen p oblem wi h eal-wo ld
cons ain s and mul iple objec i es and o model la ge de ices wi h dis ibu ed dipoles [56].
The wide a ie y o indus ial applica ions shows ha he DE is a me aheu is ic op imiza ion
algo i hm popula among p ac i ione s. In his a icle, i is used as an op imiza ion me hod o he
egis a ion o wo 2-dimensional lase ange scans.
F om an op imiza ion poin o iew, he DE e ol es a g oup (popula ion) o eal- alued ec o s
by an i e a i e applica ion o he di e en ial mu a ion and c osso e ope a ions [
55
]. So-called ial
ec o s a e in e e y i e a ion o he algo i hm c ea ed om he cu en popula ion by he di e en ial
mu a ion and ecombined wi h co esponding a ge ec o s by he c osso e ope a o . The no el
solu ions he ial ec o s ep esen a e e alua ed in he con ex o he p oblem and he ial ec o s
compe e wi h he a ge ec o s o su i al in he popula ion.
The DE p ocedu e s a s wi h a andomly cons uc ed popula ion o
N
eal– alued ec o s.
In he cou se o he e olu ion, new ial ec o s a e c ea ed as scaled pe u ba ions o exis ing
popula ion ec o s. The algo i hm c ea es ial ec o s as scaled di e ences o a minimum o wo
dis inc popula ion ec o s added o a hi d one. I a ial ec o ep esen s a be e solu ion han he
co esponding a ge ec o , i akes i s place in he popula ion.
DE’s mos impo an con ol pa ame e s a e scaling ac o and mu a ion p obabili y [
55
].
The scaling ac o ,
F∈[
0,
∞]
, a ec s he a e a which he popula ion e ol es and he c osso e
p obabili y,
C∈[
0, 1
]
, egula es he a io o elemen s ( ec o alues) ha a e ans e ed o he ial
ec o om he a ge ec o . Popula ion size,
N
and he choice o pa icula di e en ial ope a o s a e
impo an pa ame e s o he op–le el op imiza ion p ocess, oo.
The elemen a y DE ope a ions can be de ined using he ollowing equa ions [
55
]: he andom
ini ializa ion o he i h ec o o leng h Nis gi en by
~
xi[j] = and(bL
j,bU
j),j∈ {1, . . . , N}, (9)
whe e
bL
j
is he lowe bound o he
j
- h pa ame e ,
bU
j
is he uppe bound o he
j
- h pa ame e
and
and(a
,
b)
e u ns a andom numbe om he ange
[a
,
b]
. The basic di e en ial mu a ion is
de ined as
~
i=~
1+F(~
2−~
3), (10)
whe e
F
is he scaling ac o and
~
1
,
~
2
and
~
3
a e h ee dis inc ec o s selec ed andomly om
he popula ion. The ec o
~
1
is he base ec o ,
~
2
and
~
3
a e he di e ence ec o s and
~
i
is he
ial ec o .
Elec onics 2019,8, 856 16 o 20
(a) (b)
Figu e 8.
An example o scan alignmen by he CORR me hod: (
a
) Inco ec alignmen due o a o a ion
e o . (b) Co ec alignmen .
Compa isons o ansla ion and o a ion e o s o scan ma ching expe imen s in ela ion o he
leng h o he obo ajec o y be ween he scans a e shown, espec i ely, in Figu es 9and 10. I can
be seen ha he ICP algo i hm p o ides he bes alignmen o scans aken a e he obo a eled
be ween 75 mm o 450 mm. The e o o scan alignmen by ICP s a s o ise o scans aken a e he
obo a eled 750 mm o mo e. I s accu acy de e io a es e en mo e when ma ching lase ange scans
aken a e he obo a eled long dis ances, ha is, 1500 mm o 3000 mm. Based on he execu ed
scan ma ching expe imen s, he p oposed scan ma ching me hod (CORR) has o scans spaced 75 mm
o 450 mm only sligh ly wo se esul s han he ICP, s ill su icien o p ac ical indoo localiza ion.
Howe e , he CORR algo i hm shows supe io esul s when ma ching lase ange scans aken a e
he obo a eled long dis ances o 750 mm o mo e. In hese cases, i p o ides signi ican ly be e
localiza ion han he s anda d ICP algo i hm.
(a) (b)
Figu e 9.
Absolu e (
a
) and ela i e (
b
) ansla ion e o s o scan ma ching expe imen s o lase ange
scans aken a e obo mo emen o 75–3000mm.

Elec onics 2019,8, 856 17 o 20
(a) (b)
Figu e 10.
Absolu e (
a
) and ela i e (
b
) o a ion e o s o scan ma ching expe imen s o lase ange
scans aken a e obo mo emen o 75–3000mm.
Figu es 9and 10 also illus a e he con e gence o he p oposed app oach. In con as o he ICP,
RMSE and CORR a e bo h s ochas ic me hods wi h andom ini ializa ion. They we e ou pe o med by
he ICP o scans aken when he obo a eled be ween 75 and 750 mm in e ms o minimum and
a e age absolu e and ansla ion and o a ion e o s. Howe e , he igu es also clea ly illus a e ha
all independen CORR uns ha p ocessed lase ange scans aken a e he obo mo ed 1500 mm and
mo e ob ained be e a e age esul s han he ICP me hod. This sugges s ha he p oposed app oach,
al hough no de e minis ic, p oduced in hese cases, on a e age, scan alignmen s o be e quali y han
he ICP me hod.
7. Conclusions
A no el scan ma ching s a egy, based on he combina ion o c oss-co ela ion and di e en ial
e olu ion, was in oduced in his wo k. I uses c oss-co ela ion as an accu a e, obus
and compu a ionally e icien measu e o he simila i y o 2-dimensional lase ange scans
and di e en ial e olu ion o he sea ch o scan ans o ma ion pa ame e s. The p oposed scan
ma ching s a egy was implemen ed and ex ensi ely e alua ed. The e alua ion used a so wa e
amewo k o he simula ion o he mo emen o an au onomous mobile obo in an in e io .
The amewo k gene a ed a da a se composed o i ual lase ange scans, aken when he obo
ollowed a p e-de ined ajec o y in a i ual oom.
The p oposed me hod was used o ma ch lase ange scans aken by he obo a e i a eled
di e en dis ances anging om 75 mm o 3000 mm. The accu acy o he es ima ed ansla ion and
o a ion o he obo was compa ed o he accu acy o ansla ion and o a ion ob ained by a s anda d
scan ma ching algo i hm, ICP and a p e ious me hod based on a combina ion o RMSE and di e en ial
e olu ion. The expe imen s showed ha he p oposed me hod has only sligh ly lowe accu acy han
he ICP algo i hm when ma ching lase ange scans aken a e he obo a eled be ween 75 mm
and 750 mm bu i achie ed subs an ially be e esul s o scans aken a e i a eled 1500 mm o
3000 mm. The esul s o he compu a ional expe imen s sugges ha he p oposed app oach is an
accu a e and obus scan ma ching s a egy sui able in pa icula o si ua ions when he mobile obo
a els longe dis ances.
The u u e wo k will include an e icien implemen a ion o he p oposed me hod o embedded
de ices ( o example, NVIDIA Je son Nano) and ield es s wi h a physical mobile obo in a
eal en i onmen .
Au ho Con ibu ions:
Concep ualiza ion, J.K., P.K., and P.M.; Me hodology and So wa e, J.K. and P.K.;
Valida ion, J.K., P.K., and M.P.; Fo mal Analysis, J.K. and M.P; In es iga ion, J.K. and P.K.; W i ing—O iginal D a
P epa a ion, J.K., P.K, and M.P.; W i ing—Re iew & Edi ing, P.K. and P.M.; Visualiza ion, J.K.
Elec onics 2019,8, 856 18 o 20
Funding:
This wo k was suppo ed by he Eu opean Regional De elopmen Fund in he Resea ch Cen e
o Ad anced Mecha onic Sys ems p ojec , p ojec numbe CZ.02.1.01/0.0/0.0/16_019/0000867 wi hin he
Ope a ional P og amme Resea ch, and also by he p ojec s SP2019/107, “De elopmen o algo i hms and sys ems
o con ol, measu emen and sa e y applica ions V”, SP2019/135, and SP2019/141 o he S uden G an Sys em,
VSB - Technical Uni e si y o Os a a.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Re e ences
1.
Tu gu , Z.; Aydin, G.Z.G.; Se bas, A. Indoo Localiza ion Techniques o Sma Building En i onmen .
P ocedia Compu . Sci. 2016,83, 1176–1181. [C ossRe ]
2.
Za a i, F.; Gkelias, A.; Leung, K.K. A Su ey o Indoo Localiza ion Sys ems and Technologies. a Xi
2017
,
a Xi :1709.01015.
3.
Sybe eld , A.; Ayani, M.; Holm, M.; Wang, L.; Lindg en-B ews e , R. Localizing ope a o s in he sma
ac o y: A e iew o exis ing echniques and sys ems. In P oceedings o he 2016 In e na ional Symposium
on Flexible Au oma ion (ISFA), Cle eland, OH, USA, 1–3 Augus 2016; pp. 179–185. [C ossRe ]
4.
Li, J.; Bao, J.; Yu, Y. S udy on he Localiza ion o a Rescue Robo Based on Lase Scan Ma ching.
In P oceedings o he 2010 In e na ional Con e ence on Machine Vision and Human-Machine In e ace,
Kai eng, China, 24–25 Ap il 2010; pp. 642–645. [C ossRe ]
5.
Cui, Y.A.; Cai, Z.X.; Lu, W.A. Scene ecogni ion o mine escue obo localiza ion based on ision.
T ans. Non e ous Me . Soc. China 2008,18, 432–437. [C ossRe ]
6.
Wang, F.; Cui, J.Q.; Chen, B.M.; Lee, T. A comp ehensi e UAV indoo na iga ion sys em based on ision
op ical low and lase Fas SLAM. Zidonghua Xuebao/Ac a Au om. Sin. 2013,39, 1889–1900. [C ossRe ]
7.
Bonacco so, F.; Ca ania, F.; Musca o, G. E alua ion o Algo i hms o indoo mobile obo sel -localiza ion
h ough lase ange inde s da a. In P oceedings o he 7 h IFAC Symposium on In elligen Au onomous
Vehicles, Lecce, I aly, 6–8 Sep embe 2010; Volume 43, pp. 563–568.
8.
Sob ei a, H.; Cos a, C.M.; Sousa, I.; Rocha, L.; Lima, J.; Fa ias, P.C.M.A.; Cos a, P.;
Mo ei a, A.P.
Map-Ma ching Algo i hms o Robo Sel -Localiza ion: A Compa ison Be ween Pe ec Ma ch,
I e a i e Closes Poin and No mal Dis ibu ions T ans o m. J. In ell. Robo . Sys . 2018. [C ossRe ]
9.
Kaboli, A.; Bowling, M.; Musilek, P. Bayesian Calib a ion o Mon e Ca lo Localiza ion. In P oceedings o
he 21s Con e ence on A i icial In elligence (AAAI-06), Bos on, MA, USA, 16–20 July 2006; pp. 964–969.
10.
Gu, Y.; Lo, A.; Niemegee s, I. A su ey o indoo posi ioning sys ems o wi eless pe sonal ne wo ks.
IEEE Commun. Su . Tu o . 2009,11, 13–32. [C ossRe ]
11.
Maine i, L.; Pa ono, L.; Se gi, I. A su ey on indoo posi ioning sys ems. In P oceedings o he 2014
22nd In e na ional Con e ence on So wa e, Telecommunica ions and Compu e Ne wo ks (So COM), Spli ,
C oa ia, 17–19 Sep embe 2014; pp. 111–120. [C ossRe ]
12.
Guanlao, R.; Musilek, P.; Ahmad, F.; Kaboli, A. Fuzzy si ua ion based na iga ion o au onomous mobile
obo using ein o cemen lea ning. In P oceedings o he Annual Mee ing o he No h Ame ican Fuzzy
In o ma ion P ocessing Socie y (NAFIPS’04), Ban , AB, Canada, 27–30 June 2004; pp. 820–825.
13.
Fillia , D.; Meye , J.A. Map-based na iga ion in mobile obo s: I. A e iew o localiza ion s a egies.
Cogn. Sys . Res. 2003,4, 243–282. [C ossRe ]
14.
Ka ahan, M.; E kmen, A.; E kmen, I. P io i ized Mobile Robo Explo a ion Based on Pe cola ion Enhanced
En opy Based Fas SLAM. J. In ell. Robo . Sys . Theo y Appl. 2013,75, 541–567. [C ossRe ]
15.
Dumble, S.; Gibbens, P. E icien Te ain-Aided Visual Ho izon Based A i ude Es ima ion and Localiza ion.
J. In ell. Robo . Sys . 2015,78, 205–221. [C ossRe ]
16.
Bosse, M.; Zlo , R. Map ma ching and da a associa ion o la ge-scale wo-dimensional lase scan-based
SLAM. In . J. Robo . Res. 2008,27, 667–691. [C ossRe ]
17.
Co so, N.; Zakho , A. Indoo localiza ion algo i hms o an ambula o y human ope a ed 3D mobile mapping
sys em. Remo e Sens. 2013,5, 6611–6646. [C ossRe ]
18.
Ho nung, A.; Oßwald, S.; Maie , D.; Bennewi z, M. Mon e ca lo localiza ion o humanoid obo na iga ion
in complex indoo en i onmen s. In . J. Humanoid Robo . 2014,11, 1441002. [C ossRe ]
19.
Ku ecka, A.; Konecny, J.; P auzek, M.; Kozio ek, J. Mon e ca lo based wi eless node localiza ion.
Elek on. I Elek o ech. 2014,20, 12–16. [C ossRe ]
Elec onics 2019,8, 856 19 o 20
20.
Jiang, Z.; Zhou, W.; Li, H.; Mo, Y.; Ni, W.; Huang, Q. A New Kind o Accu a e Calib a ion Me hod o Robo ic
Kinema ic Pa ame e s Based on he Ex ended Kalman and Pa icle Fil e Algo i hm.
IEEE T ans. Ind. Elec on.
2018,65, 3337–3345. [C ossRe ]
21.
Dellae , F.; Fox, D.; Bu ga d, W.; Th un, S. Mon e Ca lo localiza ion o mobile obo s.
P oc. IEEE In . Con . Robo . Au om. 1999,2, 1322–1328.
22.
Weike sdo e , D.; Ad ian, D.B.; C eme s, D.; Con ad , J. E en -based 3D SLAM wi h a dep h-augmen ed
dynamic ision senso . In P oceedings o he IEEE In e na ional Con e ence on Robo ics and Au oma ion,
Hong Kong, China, 31 May–7 June 2014; pp. 359–364.
23.
Chen, Y.; Tang, J.; Jiang, C.; Zhu, L.; Leh omäki, M.; Kaa inen, H.; Kaijaluo o, R.; Wang, Y.; Hyyppä, J.;
Hyyppä, H.; e al. The accu acy compa ison o h ee simul aneous localiza ion and mapping (SLAM)-based
indoo mapping echnologies. Senso s 2018,18, 3228. [C ossRe ] [PubMed]
24.
Ba dow, P.; Da ison, A.J.; Leu enegge , S. Simul aneous op ical low and in ensi y es ima ion om an
e en came a. In P oceedings o he IEEE Compu e Socie y Con e ence on Compu e Vision and Pa e n
Recogni ion, Las Vegas, NV, USA, 27–30 June 2016; Volume 2016, pp. 884–892.
25.
He mand, E.; Nguyen, T.; Hosseinzadeh, M.; Ga one, E. Cons ained Con ol o UAVs in Geo encing
Applica ions. In P oceedings o he MED 2018 26 h Medi e anean Con e ence on Con ol and Au oma ion
(MED), Zada , C oa ia, 19–22 June 2018; pp. 217–222.
26.
Balles e os-Escamilla, M.; C uz-O iz, D.; Chai ez, I.; Lu iano-Juá ez, A. Adap i e ou pu con ol o a mobile
manipula o hanging om a quadcop e unmanned ehicle. ISA T ans. 2019. [C ossRe ]
27.
F iedman, C.; Chop a, I.; Rand, O. Pe ime e -Based Pola Scan Ma ching (PB-PSM) o 2D Lase Odome y.
J. In ell. Robo . Sys . Theo y Appl. 2015,80, 231–254. [C ossRe ]
28.
Pa k, S.; Pa k, S.K. Global localiza ion o mobile obo s using e e ence scan ma ching.
In . J. Con ol. Au om. Sys . 2014,12, 156–168. [C ossRe ]
29.
Gao, Y.; Liu, S.; A ia, M.; Nou eldin, A. INS/GPS/LiDAR in eg a ed na iga ion sys em o u ban and indoo
en i onmen s using hyb id scan ma ching algo i hm. Senso s 2015,15, 23286–23302. [C ossRe ]
30.
Diosi, A.; Kleeman, L. Fas Lase Scan Ma ching using Pola Coo dina es. In . J. Robo . Res.
2007
,
26, 1125–1153. [C ossRe ]
31.
Rusinkiewicz, S.; Le oy, M. E icien a ian s o he ICP algo i hm. In P oceedings o he Thi d In e na ional
Con e ence on 3-D Digi al Imaging and Modeling, Québec Ci y, QC, Canada,
28 May–1 June 2001;
pp. 145–152.
32.
Teza, G.; Galga o, A.; Zal on, N.; Gene ois, R. Te es ial lase scanne o de ec landslide displacemen
ields: A new app oach. In . J. Remo e Sens. 2007,28, 3425–3446. [C ossRe ]
33.
Ishii, M.; Yokoyama, K. Mapping and co ec ion me hod in s a ic en i onmen s o au onomous mobile
obo . In . J. Soc. Ma e . Eng. Resou . 2014,20, 207–212. [C ossRe ]
34.
Zezhong, X.; Jilin, L.; Zhiyu, X. Scan ma ching based on CLS ela ionships. In P oceedings o he
IEEE In e na ional Con e ence on Robo ics, In elligen Sys ems and Signal P ocessing, Changsha, China,
8–13 Oc obe 2003; Volume 1, pp. 99–104.
35.
Webe , J.; Jö g, K.W.; on Pu kame , E. APR—Global Scan Ma ching Using Ancho Poin Rela ionships.
In P oceedings o he In elligen Au onomous Sys ems (IAS-6), Venice, I aly, 25–27 July 2000.
36.
Sun, Q.; Yuan, J.; Zhang, X.; Sun, F. RGB-D SLAM in Indoo En i onmen s wi h STING-Based Plane Fea u e
Ex ac ion. IEEE/ASME T ans. Mecha on. 2018,23, 1071–1082. [C ossRe ]
37.
Li, J.; Zhong, R.; Hu, Q.; Ai, M. Fea u e-based lase scan ma ching and i s applica ion o indoo mapping.
Senso s 2016,16, 1265. [C ossRe ]
38.
P ie o, P.G.; Ma in, F.; Mo eno, L.; Ca ballei a, J. DENDT: 3D-NDT scan ma ching wi h Di e en ial E olu ion.
In P oceedings o he 2017 25 h Medi e anean Con e ence on Con ol and Au oma ion,
MED 2017,
Valle a,
Mal a, 3–6 July 2017; pp. 719–724.
39.
Bibe , P.; S asse , W. The no mal dis ibu ions ans o m: A new app oach o lase scan ma ching.
In P oceedings o he 2003 IEEE/RSJ In e na ional Con e ence on In elligen Robo s and Sys ems (IROS 2003)
(Ca . No.03CH37453), Las Vegas, NV, USA, 27–31 Oc obe 2003; Volume 3, pp. 2743–2748.
40.
Ma in, F.; T iebel, R.; Mo eno, L.; Siegwa , R. Two di e en ools o h ee-dimensional mapping: DE-based
scan ma ching and ea u e-based loop de ec ion. Robo ica 2014,32, 19–41. [C ossRe ]
41.
Mi khani, M.; Fo sa i, R.; Shah i, A.M.; Moayedikia, A. A no el e icien algo i hm o mobile obo
localiza ion. Robo . Au on. Sys . 2013,61, 920–931. [C ossRe ]
Elec onics 2019,8, 856 20 o 20
42.
Konecny, J.; P auzek, M.; K ome , P.; Musilek, P. No el Poin - o-Poin Scan Ma ching Algo i hm Based on
C oss-Co ela ion. Mob. In . Sys . 2016,2016, 6463945. [C ossRe ]
43.
Konecny, J.; P auzek, M.; Hla ica, J. SLAM algo i hm based on c oss-co ela ion scan ma ching.
In P oceedings o he 8 h In e na ional Con e ence on Signal P ocessing Sys ems, Auckland, New Zealand,
21–24 No embe 2016; ACM In e na ional Con e ence P oceeding Se ies; pp. 89–93.
44.
K ome , P.; Konecny, J.; P auzek, M. Poin -based scan ma ching by di e en ial e olu ion. In P oceedings o
he 2016 In e na ional Con e ence on In elligen Ne wo king and Collabo a i e Sys ems, IEEE INCoS 2016,
Os aw a, Czech Republic, 7–9 Sep embe 2016; pp. 215–221.
45.
Konecny, J.; P auzek, M.; Hla ica, J. Indoo LiDAR Scan Ma ching Simula ion F amewo k o
In elligen Algo i hms E alua ion. In P oceedings o he Fi s In e na ional Scien i ic Con e ence
“In elligen In o ma ion Technologies o Indus y” (IITI’16), Sochi, Russia, 16–21 May 2016; Ad ances in
In elligen Sys ems and Compu ing; Volume 451, pp. 355–364.
46.
Ko zian, J.; Konecny, J.; P okop, H.; Lippa, T.; Ku uc, M. Au onomous explo a i e mobile obo :
Na iga ion and cons uc ion. In P oceedings o he 9 h RoEduNe IEEE In e na ional Con e ence,
RoEduNe 2010, Sibiu, Romania, 24–26 June 2010; pp. 49–54.
47. ARM In o ma ion Cen e . A ailable online: h p://in ocen e .a m.com (accessed on 15 July 2019).
48.
Wen, J.; Qian, C.; Tang, J.; Liu, H.; Ye, W.; Fan, X. 2D LiDAR SLAM Back-End Op imiza ion wi h Con ol
Ne wo k Cons ain o Mobile Mapping. Senso s 2018,18, 3668. [C ossRe ]
49.
Wang, Z.; Chen, Y.; Mei, Y.; Yang, K.; Cai, B. IMU-Assis ed 2D SLAM Me hod o Low-Tex u e and Dynamic
En i onmen s. Appl. Sci. 2018,8, 2534. [C ossRe ]
50.
Wang, W.; Saku ada, K.; Kawaguchi, N. Re lec ance In ensi y Assis ed Au oma ic and Accu a e Ex insic
Calib a ion o 3D LiDAR and Pano amic Came a Using a P in ed Chessboa d. Remo e. Sens.
2017
,9, 851.
[C ossRe ]
51.
Besl, P.J.; McKay, N.D. A Me hod o Regis a ion o 3-D Shapes. IEEE T ans. Pa e n Anal. Mach. In ell.
1992
,
14, 239–256. [C ossRe ]
52.
Konecny, J.; P auzek, M.; Hla ica, J. ICP Algo i hm in Mobile Robo Na iga ion: Analysis o Compu a ional
Demands in Embedded Solu ions. IFAC-Pape sOnLine 2016,49, 396–400. [C ossRe ]
53.
Hazewinkel, M. Encyclopaedia o Ma hema ics: Monge—Ampè e Equa ion—Rings and Algeb as; Encyclopaedia o
Ma hema ics; Sp inge New Yo k, NK, USA, 1995.
54.
Tan, C.C.; Hi d, C.; Okada, Y. P ocessing o sound ield signal o a cons ained panel by c oss-co ela ion.
In P oceedings o he In e na ional Con e ence on In o ma ion, Communica ions and Signal P ocessing,
ICICS, Singapo e, 12 Sep embe 1997; Volume 1, pp. 316–320.
55. Yang, X. Na u e-Inspi ed Op imiza ion Algo i hms; Else ie : Ams e dam, The Ne he lands, 2014.
56.
Das, S.; Mullick, S.S.; Sugan han, P. Recen ad ances in di e en ial e olu ion—An upda ed su ey.
Swa m E ol. Compu . 2016,27, 1–30. [C ossRe ]
c
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