Optoelectronic properties of silver doped copper oxide thin films

Vishal Mohade1, Krishna Kumar1 Parasuraman Swaminathan1,2*

1Electronic Materials and Thin Films Lab, Dept. of Metallurgical and Materials
Engineering,

Indian Institute of Technology, Madras, Chennai, India

2Centre of Excellence in Ceramics Technologies for Futuristic Mobility,

Indian Institute of Technology Madras, Chennai, India

*Email<EMAIL_ADDRESS>
## Abstract

Thin films have found a wide variety of applications because of the
substantial improvement in their properties as compared to bulk metals. Metal
oxide thin films are increasingly being used in various fields and are
especially important in functional applications. They can be either $p$\- or
$n$-type in nature depending on the materials, dopants, and preparation route.
Copper oxide is an example of a $p$-type metal oxide, which finds application
in solar cells, photo-electrochemical cells, gas sensors, supercapacitors, and
thermoelectric touch detectors. Both copper (I) and copper (II) oxides can be
grown with the lower valence state oxide stable at low temperature and the
higher valence state obtained by annealing at higher temperatures. In this
work, we modify the optical and electrical properties of copper oxide thin
films, by doping of silver through a thermal evaporation process route. Copper
is thermally evaporated onto the substrate and silver is co-evaporated during
this process. The films are then annealed in ambient under various conditions
to obtain copper oxide. Structural and functional comparison is made between
undoped and silver doped copper oxide thin films, prepared under the same
conditions. Thermal evaporation is a simple route for obtaining doped metal
oxides and the process can be extended to a variety of other systems as well.

Keywords: Copper oxide; Thermal evaporation; Optoelectronic properties;
Electron microscopy; Silver doping

##  1 Introduction

Copper oxide is a well-studied material because of the abundance of copper in
nature, its $p$-type conductivity, easy synthesis by oxidation of copper, good
optical and electrical properties, and non-toxic nature. There are various
methods to produce copper oxide thin films viz. thermal evaporation [1, 2, 3,
4], magnetron sputtering[5], electrodeposition[6, 7, 8, 9], chemical vapor
deposition [10], chemical bath deposition [11, 12, 13], plasma sputtering
[14], molecular beam epitaxy, DC reactive sputtering[15], RF reactive
sputtering[16, 17], ion beam sputtering [18], sol-gel [19, 20], and pulsed
laser deposition[21].

There have been several studies to determine the properties of copper oxide
thin films. Pure copper film on annealing is found to form different oxides at
different annealing temperatures. The first oxide is cuprous oxide (Cu2O),
which starts forming in range of 200-250 °C and exhibits and optical bandgap
of 2.0-3.0 eV, with cubic crystal structure of lattice parameter 0.427 nm. The
higher valence, cupric oxide (CuO) starts forming above 300 °C and has a
optical bandgap of 1.2-1.7 eV. CuO shows monoclinic crystal structure and both
oxides show $p$-type conductivity [1, 5, 4]. These oxides shows promising
applications in gas sensors[22, 23, 24], solar cells[15, 25, 26],
thermoelectric touch sensors[2], thin film transistors[3], and
supercapacitors[11], to name a few. Thermal evaporation produces very uniform
films with no porosity, and high adhesion. It is a non-toxic and line of sight
process.

The Cu-Ag phase diagram [27] shows a eutectic obtained at 71.9 wt. % Ag. For
temperatures below 400 °C and very low concentration of Ag there is negligible
mixing or solubility of Ag in Cu. The pressure vs. temperature diagram for the
Cu-O system [28] shows that at a pressure greater than 100 Torr and
temperatures higher than 600 °C, copper oxide exists as CuO. Papadimitropolous
et al. deposited copper oxide thin films using thermal vacuum evaporator on a
silicon substrate [4]. On oxidation, the film showed cuprous oxide formation
at 225 °C, copper silicides were also seen at this temperature. At 280 °C,
Cu2O amount starts to decrease and CuO peaks appear, which then converts to
only CuO peaks at 350 °C. CuO forms because the Gibbs free energy for the
oxidation of Cu2O to CuO at a temperature of 200 °C is -3.73 kcal$/$mol [29].
Chaudhary et al. justified it as the supply of thermal energy to the cubic
Cu2O should cause higher ionicity and smaller grain size to transform into
lower symmetry and larger grain size [30]. Figuieredo et al. observed similar
peaks of Cu2O (111) from 250 to 300 °C and CuO (11-1) above 300 °C by using
e-beam evaporation of pure copper sample on glass slide followed by annealing
[2]. Thus, the overall conversion can be written as

$Cu\rightarrow(Cu\;+\;Cu_{2}O)\rightarrow
Cu_{2}O\rightarrow(Cu_{2}O+CuO)\rightarrow CuO$ (1)

In this work we attempted addition of silver nanoparticles on the surface of a
copper thin film without breaking vacuum. We used a thermal evaporation
process route to ascertain efficient film morphology for study of the
functional properties. The as deposited samples were then annealed to obtain
oxides. The study of morphology helped us to understand grain development with
temperature. A variety of characterization tools were used to study the
effects of silver addition. The optical properties showed the bandgap values
of copper oxide similar to others. Similar work has been attempted by only one
other researcher, who used microwave annealing process to study optical
properties of silver doped copper oxide thin film [31]. Li-doped copper oxide
thin films also shows a decrease in band gap with Li concentration
[chand2014structural]. The doping process for copper oxide thin film has not
been adapted elsewhere. The effect on electrical properties because of doping
copper oxide have not yet been reported. This work will give a brief
information about changes in resistance and carrier concentration by silver
doping. The effect of temperature on resistance of copper oxide thin film can
also help to develop a temperature sensor. These properties were studied
elsewhere with computational modelling using density functional theory [32].

##  2 Materials and methods

Copper thin films were deposited on microscopic glass slides using high vacuum
coating unit (Model HPVT 303) by Hydro Pneo Vac Technology. Prior to
deposition, the glass slides were cut to dimension of 2.5 $\times$ 2.5 cm2.
Then they were cleaned in steps of 1 % soap solution, deionized water, ethanol
and deionized water again by ultra-sonication for 15 min in each solution.
These were dried by wiping with lint free cloth. The deposition was performed
at high vacuum level ($7\times 10^{-6}$ mbar). The rate of deposition was
maintained for all depositions to be 0.14 nm s-1. Thin film thickness was
monitored with a quartz crystal microbalance. The substrate was kept at room
temperature and no external heating was provided during deposition, though
there was a rise in temperature of the substrate during thermal evaporation.
Silver thin film of thickness 1 nm were deposited on top of the pure copper
film, without breaking vacuum. The deposited thin film was then annealed at
temperatures from 150 to 450 °C at an interval of 100 °C. The annealing was
performed in a muffle furnace in ambient atmosphere. The heating rate was
maintained at 5 °C/min and the holding time was 2 h. Both pure copper and
silver doped copper films were annealed under the same conditions.

Grazing incidence x-ray diffraction (GIXRD) measurements were performed on a
Rigaku Smartlab XRD machine with 9 kW rotating anode X-ray source. The
configuration includes Cu as the source material and Ge monochromator. The
incidence angle was maintained at 1 °and $2\theta$ was varied at the scanning
rate of 0.01 °per s. The analysis was done using XPert Highscore pro.cUV-
Visible spectroscopy was performed on a Jasco V-730 spectrophotometer, with
halogen and deuterium lamps as sources. The wavelength range for measurement
was 200 – 1100 nm. Raman spectroscopy was performed using NdYAG laser of
wavelength 532 nm on WiTech alpha 300 confocal Raman microscope. The
accumulation time was kept at 5 s. The objective used was 20 $\times$. For
photoluminescence spectroscopy (PL) Jasco FP 6300 was used. The excitation
wavelengths used were 320 nm and 450 nm. A DC powered 150 W Xe lamp was used
as a source. The accumulation and integration time were set at 10 s
respectively. Electrical transport measurement was carried out in Van der Pauw
setup on DynaCool PPMS by Quantum design at room temperature. All measurements
were done at 300 K. The contacts were made using silver paint adhesive and
copper wire. The sample dimensions were maintained at 4 mm $\times$ 4mm
($L\times W$). $I-V$ measurements were performed in a four-probe setup on a
source meter, Keysight precision measurement system. The contacts were made
using silver epoxy adhesive and copper wires. Voltage range was kept as -10 V
to 10 V. $I-V$ measurement with temperature (Seebeck coefficient) was done on
Cascade Microtech summit 12000 AP. The temperature range was from room
temperature to 120 °C in steps of 10 °C and ETC 200L (Espec corp.) thermos
chuck was used to monitor temperatures. The voltage range was -10 to 10 V.
Sheet resistance was measured on Jandel mode RM 3000 using a four probe
configuration. The equipment was calibrated and zeroed before taking readings.
The current was automatically set by equipment within range of 10 nA to 99.99
mA. Scanning electron microscopy was done on FEI Quanta 400 high resolution
scanning electron microscope. The detector used was Everhart Thornley detector
(ETD). Transmission electron microscopy was performed on FEI Tecnai 12
electron microscope.

##  3 Results and Discussion

###  3.1 Structural characterization

On annealing of samples, visually, we can clearly deduce that the sample with
250 °C annealing temperature was the most transparent. Annealing at lower
temperatures, 150 °C, produced samples which were opaque, while at the highest
temperature of 450 °C, the annealed sample was more transparent than 350 °C
annealed sample. The optical images are summarized in figure 1 and the samples
are kept above IITM logo for showcasing their transparency.

Figure 1: Comparison of optical images of annealed pure copper oxide and
silver doped copper oxide thin films.

To identify the phases, XRD studies were carried out on copper oxide and
silver doped copper oxide thin films. The XRD patterns were measured for thin
films annealed at temperatures from 150 to 450 °C. GIXRD results, presented in
figure 2 (a) and (b), showed the presence of copper peaks in 150 °C annealed
sample (ICDD number: 01-085-1326), indicating incomplete oxidation at this
temperature. Samples annealed at 250 °C showed peaks at 36.5 °corresponding to
Cu2O (111) and at 42.2 °corresponding to Cu2O (200) (ICDD number: 05-667).
Samples annealed at 350 °C showed peaks at 35.5 °and 38.7 °corresponding to
CuO [ICDD number: 45-0937] and samples annealed at 450 °C showed 35.5 °and
38.7 °peaks. At 150 °C, a copper peak appears at 42.4 °, from Cu (111) plane.
The data obtained matches results are obtained by Choudhary et al.[1].

Figure 2: GIXRD of a) undoped copper oxide b) silver doped copper oxide thin
film at different annealing temperatures.

The crystallite size variation with temperature and doping can be seen in
table 1. The crystallite size was obtained using Hall–Petch equation. For
undoped copper oxide thin films the crystallite size decreases with annealing
temperature, whereas for Ag doped copper oxide it increases. Ag doping has
decreased the crystallite size in films annealed at 150 and 250 °C, when
compared to undoped Cu at these temperatures. This is due to higher affinity
of copper towards oxygen and the preferential oxidation of copper that occurs
in presence of silver [31].

$Ag_{2}O\,(s)\;+\;Cu\,(s)\rightarrow CuO\,(s)\;+\;2Ag\,(s)$ (2)

Table 1: Variation of crystallite size with temperature.
Annealing | Crystallite size of | Crystallite size of
---|---|---
temperature (°C) | undoped copper oxide (nm) | silver doped copper oxide (nm)
150 | 33.7 | 5.2
250 | 13 | 6.3
350 | 8.3 | 18.8
450 | 10.6 | 15.2

SEM was performed at magnification of 40000 $\times$ in secondary electron
mode using a Everhart–Thornley detector. Thin films were sputtered with gold
before measurement. Typical microstructure of the thin films, without and with
silver, analyzed by SEM are shown figures 3 and 4 respectively. The inset at
the bottom left shows the calibration scale to observe the grain size and top
right shows the temperature of annealing. Both thin films annealed at 150 °C
shows smoother film and very fine grain size and closed packed structure. The
grain size increases with annealing temperature. Figure 3 shows undoped copper
oxide thin films annealed at different temperatures. The film morphology
appears smooth and grain size distribution is uniform. Thin films annealed at
350 °C shows very high increase in grain size as compared to other films. The
film annealed at 450 °C shows presence of pores smaller than the grains. Ag
doped SEM images, on the other hand, shows smooth and uncracked films. The
grains appear well-defined in Ag doped copper oxide thin film (shown in figure
4) and the grain size increases with temperature, which is similar to the
undoped copper oxide thin film. The grains agglomerated to form bigger grains,
therefore grain size variation in the 450 °C annealed film looks non uniform.
A crack is also observed around bigger grains. This crack is due to connecting
of adjoining pores. The pore size observed is comparable to the grain size.
The 350 °C film shows more layered structure and decreased pore size. On
comparing to undoped copper oxide thin film annealed at 450 °C in figure 3,
the Ag doped thin film shows aggregated grains with more defined shape of top
layer.

Figure 3: SEM images of pure copper oxide thin film annealed at 150, 250, 350,
and 450 °C. Figure 4: SEM images of Ag doped copper oxide thin film annealed
at 150, 250, 350, and 450 °C.

To get closer look at the grain structure on the addition of silver to copper
thin films, representative TEM images of the as deposited copper and silver
doped copper thin films are shown in figure 5. Figure 5 (a) shows a uniform
grain size for pure copper, whereas in figure 5 (b) the grain size is non
uniform and there are some grains which are distributed randomly with larger
size as compared to rest of the grains and the smaller grains shows similar
size as in fig 5 (a). By comparison between (a) and (b) we can conclude that
the bigger grains are of Ag doped copper.

Figure 5: TEM image of a representative sample of a) pure copper and b) silver
doped copper

###  3.2 Optical properties

Figure 6: Variation of absorbance with wavelength for a) pure copper oxide
thin film and b) silver doped copper oxide thin film.

Figure 6 shows the absorbance plot for both doped and undoped copper oxide
thin films. The absorbance is high in the UV region due to the opaque nature
of the thin film. Silver doped thin film shows higher absorbance in blue
region as compared to undoped copper oxide. This may be due to the nature of
noble metals such as silver. They absorb light due to the transition of
electrons between unoccupied hybridized $sp$ states and occupied $d$ states.
Absorbance decreases with increase in wavelength till 500 nm (blue green
region) for undoped thin film. A similar behavior is shown by silver doped
copper oxide annealed at 250 °C. The optical band gap of copper oxide thin
films can be calculated using Tauc equation and figure 7 shows the Tauc plot
for determining the band gap of CuO and Ag doped CuO thin films. Band gap
values can be seen from the extrapolation of the linear portion of to the
energy axis of the Tauc plot (arrow pointing on $X$-axis). Cu2O has a direct
band gap of 2.91 $\pm$ 0.3 eV and CuO has indirect band gap of 1.5 $\pm$ 0.3
eV. The data obtained is similar to those obtained in literature [1, 3, 2].
The band gap of silver doped Cu2O is 3.04 $\pm$ 0.3 eV and CuO is 1.70 $\pm$
0.3 eV.

Figure 8 shows Raman spectra of annealed copper oxide thin films. Among nine
optical modes of CuO, three are Raman active ($A_{g}$\+ 2 $B_{g}$). The peaks
298, 342 and 627 cm-1 corresponds to CuO and the peaks 143, 210, and 617 cm-1
correspond to Cu2O. 450 °C Ag doped copper oxide thin film shows all three CuO
peaks only. On the other hand, other temperatures show the presence of Cu2O
peaks more dominantly. The silver doped copper oxide thin film annealed at 250
°C shows the greatest intensity of peaks at 143 and 210 cm-1. This can be
attributed to the presence of Cu2O. Raman data confirms the results obtained
by XRD. Undoped and doped copper oxide films annealed at 150 °C shows only one
peak corresponding to Cu2O at 1100 cm-1. This signifies the presence of very
thin oxide layer, although no other peaks are available. This can suggest that
the oxide formation has not started properly at 150 °C.

Figure 7: Tauc plot for undoped and Ag doped Copper oxide thin films. Figure
8: Raman spectra of annealed a) undoped copper oxide and b) silver doped
copper oxide thin films.

Photoluminescence spectra were also recorded for the undoped and doped copper
oxide thin films. The film annealed at 250 °C shows peaks at 398 nm (near UV
emission) and 496 nm (corresponding to cyan emission). The peaks at 540 and
578 nm correspond to green and yellow emissions respectively. The presence of
high yellow peaks indicates excess oxygen whereas green emissions indicates
oxygen deficiency [33, 34]. Both doped and undoped copper oxide thin films
annealed at 450 °C exhibit emission in UV range i.e. 364 nm, which can be
correlated to band gap transition in CuO [34]. The green emissions are also
associated with the presence of surface defects and transition of carriers
from near conduction band (oxygen vacancies) to deep valence band (Cu
vacancies). Figure 9 shows PL spectra for undoped and doped copper oxide thin
films at an excitation wavelength 450 nm. The graph shows a single red
emission, this can be due to neutral and single ionized oxygen transitions or
deep level emission related to presence of defect [35, 36].

Figure 9: Photoluminescence (PL) spectra of a) undoped copper oxide thin film
and b) silver doped copper oxide thin film with an excitation wavelength 450
nm.

###  3.3 Electrical properties

Electrical transport measurements were performed with Van der Pauw method to
obtain carrier concentrations. It shows the resistance value obtained for
undoped copper oxide thin films annealed at 250 and 450 °C are 12-20 M$\Omega$
and 2.8 M$\Omega$ respectively. For silver doped thin film, annealed at 450
°C, the corresponding value was 22-30 k$\Omega$. The carrier concentration
values for undoped Cu2O thin film were in range of $10^{15}$ cm-3 and for
doped CuO in range of $10^{16}$ cm-3. The nature of the Hall coefficient shows
$p$-type conductivity in copper oxide thin films [3, 2, 5].

Table 2 shows the sheet resistance values obtained by four probe measurement.
The films annealed at 150 °C showed same resistance as copper because of
negligible surface oxidation. The resistance is very low for undoped copper
oxide thin films as compared to silver doped copper oxide thin films. The
increase in resistance is due to increased scattering centers by the addition
of silver.

Table 2: Sheet resistance values obtained by four probe measurement.
Annealing | Undoped copper oxide | Silver doped copper oxide
---|---|---
temperature (°C) | ($\Omega/sq.$) | ($\Omega/sq.$)
150 | 1.2 | 1.1
250 | $4\times 10^{6}$ | $66\times 10^{6}$
350 | $10\times 10^{6}$ | $24.7\times 10^{6}$
450 | $1.3\times 10^{6}$ | $19\times 10^{6}$

The $I-V$ curves were also obtained for undoped and silver doped copper oxide
thin films. The undoped copper oxide thin film annealed at 450 °C shows non-
linear behavior, while the other samples showed Ohmic behavior. The resistance
values obtained were similar to those obtained by four-probe data. The
temperature dependence of resistance was also measured and the values are
listed in table 3. The table shows that the resistance decreases with increase
in temperature for all the annealed thin films. The drop in the resistance for
silver doped thin film annealed at 250 °C is very drastic, but the initial
resistance value is very high which also can be seen the from table. This
decrease is not regular for undoped copper oxide thin film annealed at 250 °C.
The decrease for silver doped thin film annealed at 450 °C is gradual with
temperature, which makes it a great choice for temperature sensor application.

Table 3: Resistance variation with temperature for select annealed copper
oxide thin films.
Temperature | Resistance of | Resistance of | Resistance of
---|---|---|---
(°C) |  Cu 250 °C (M$\Omega$) |  Cu-Ag 250 °C (M$\Omega$) |  Cu-Ag 450 °C (M$\Omega$)
22 | 33.3 | 203 | 14\. 7
50 | 9.05 | 92.7 | 9.37
60 | 17.9 | 69 | 8.02
70 | 6.66 | 52.3 | 6.71
80 | 8.87 | 42.1 | 6.1
90 | 5.95 | 30.5 | 5.49
100 | 6.34 | 23.1 | 4.61

##  4 Conclusion

Copper oxide thin film annealed at 250 °C shows the highest optical
transparency. XRD studies shows the presence of Cu2O phase in both undoped and
silver doped copper oxide thin films annealed at 250 °C. CuO phase starts
forming above 330 °C and hence it is visible in XRD pattern of thin films
annealed at 350 and 450 °C. Raman spectroscopy also confirm the results
obtained by XRD. On increasing the annealing temperature, the grain size
increased. Silver doped copper oxide thin films showed larger band gap than
undoped copper oxide thin films. The blue and green emission showed deficiency
or excess of oxygen in thin films, and red emission showed transition of
single and ionized oxygen. Copper oxide thin films showed $p$-type
conductivity. Silver doped copper oxide thin films showed higher resistance
than undoped copper oxide. The resistance value decreases with increase in
temperature for all copper oxide thin films. The resistance variation of
silver doped copper oxide thin film annealed at 450 °C with temperature showed
a possible application as temperature sensor.

## Acknowledgments

Support from the Centre of Excellence in Ceramics Technologies for Futuristic
Mobility (project number SB22231272MMETWO008702) is acknowledged. Electron
microscopy (SEM and TEM) was carried out at the facilities available in the
Dept. of Metallurgical and Materials Engineering, IIT Madras. Optical
characterisation was performed at the facilities available at the Dept. of
Physics, IIT Madras, while electrical characterisation was carried out at the
Centre for NEMS and Nanophotonics, IIT Madras.

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11institutetext: University of Engineering and Technology, Vietnam National
University
Hanoi, Vietnam<EMAIL_ADDRESS>{canhthanh, dongocminh,
<EMAIL_ADDRESS>
∗ Corresponding author

# Fusion LiDAR-Inertial-Encoder data for High-Accuracy SLAM

Manh Do Duc  Thanh Nguyen Canh  Minh DoNgoc  Xiem HoangVan∗

###### Abstract

In the realm of robotics, achieving simultaneous localization and mapping
(SLAM) is paramount for autonomous navigation, especially in challenging
environments like texture-less structures. This paper proposed a factor-graph-
based model that tightly integrates IMU and encoder sensors to enhance
positioning in such environments. The system operates by meticulously
evaluating the data from each sensor. Based on these evaluations, weights are
dynamically adjusted to prioritize the more reliable source of information at
any given moment. The robot’s state is initialized using IMU data, while the
encoder aids motion estimation in long corridors. Discrepancies between the
two states are used to correct the IMU drift. The effectiveness of this method
is demonstrably validated through experimentation. Compared to Karto SLAM, a
widely used SLAM algorithm, this approach achieves an improvement of 26.98% in
rotation angle error and a reduction of 67. 68% in position error. These
results convincingly demonstrate the method’s superior accuracy and robustness
in textureless environments.

###### Keywords:

SLAM Fusion sensor ROS Factor Graph.

##  1 Introduction

The field of Autonomous Mobile Robots (AMRs) is experiencing a surge of
development across diverse industries such as healthcare, security monitoring
[1], [2], and construction [3]. To thrive in these dynamic environments and
fulfill their designated tasks, AMRs necessitate robust capabilities in three
critical areas: information gathering [4], environment perception [5], and
precise Simultaneous Localization and Mapping (SLAM) [6], [7], [8]. Although
various research efforts have explored effective mapping techniques that
utilize individual sensors such as LiDAR [9] or cameras [10], cameras have
significant limitations. Their sensitivity to light fluctuations can
considerably hinder reliable operation. To address this challenge, this paper
delves into a LiDAR-based approach for SLAM. LiDAR offers substantial
advantages, including a marked reduction in susceptibility to variations in
lighting conditions and the ability to operate at high frequencies. However,
established 2D LiDAR-based mapping methods, such as GMapping and Hector SLAM,
showcase success primarily in controlled indoor environments [11]. These
methods struggle to adapt to environments characterized by sparsity, featuring
long corridors, tunnels, or open spaces.

To address these limitations of single sensors, recent research has explored
multi-sensor fusion techniques by leveraging the strengths of complementary
sensors. LIO-SAM [12] integrates an IMU not only to predict robot motion prior
to LiDAR scan matching, but also to initiate the LiDAR odometry optimization
process. This combined approach refines IMU sensor error estimates within a
factor graph. Several previous works [13], [14] proposed a multimodal system
that integrates LiDAR, camera, IMU, encoder, and GPS to estimate the robust
and accurate state of the robot. It can also eliminate dynamic targets and
unstable features. Overall, tightly coupled multi-sensor fusion systems are
becoming essential for ensuring the accuracy and flexibility required for
autonomous robots operating in complex environments.

This paper proposes an effective method that tightly integrates data from
multiple sensors, including LiDAR, IMUs, and encoders, to estimate robot
states using factor graphs. Our key advantages include: (1) sensor uncertainty
detection, which is estimated when the robot moves in a new scenario with each
sensor, (2) adaptive noise assignment- it can adjust for noise levels based on
the sensor uncertainty detection part, and (3) reconfigurable optimization,
which can automatically reconfigure the pose graph optimization process
throughout robot operation. We evaluated our proposed method through physical
simulations, demonstrating its accuracy and applicability in the real
environment.

##  2 Methodology

Figure 1: Pipeline of our method.

The pipeline of the method is shown in Fig. 1 and contains two nodes. Our
robot utilizes three sensors: 2D LiDAR generates a 2D point cloud, providing a
detailed representation of the surrounding environment; the IMU measures the
robot’s angular velocity and linear acceleration, aiding in motion estimation;
the encoder tracks the distance traveled by the robot. Sensor preprocessing
involves data caching and synchronization to ensure consistency. Raw IMU data
are used to estimate robot motion and pre-integrated according to the time
stamp to remove the motion distortion of the point cloud. In addition, the
sensor can detect degradation and update the weight during movement. Robot
state estimation employs a maximum a posteriori (MAP) approach with a factor
graph to model robot position and trajectory based on sensor measurements.
Finally, a 2D map of the environment is constructed using the processed LiDAR
data.

Although multisensor systems offer improved positioning accuracy by
incorporating various sensors, it is crucial to strike a balance. An increase
in the number of sensors directly results in higher computational complexity.
In addition, not all sensors perform well in every environment. Including an
inappropriate sensor can negatively impact the state estimation process.
Therefore, careful sensor selection is vital for multi-sensor systems. Our
experiments revealed that LiDAR performance degrades in highly repetitive
environments such as corridors and tunnels. To address this, we analyze the
distance difference between consecutive LiDAR scans. If this difference falls
below a predefined threshold, it indicates potential LiDAR degradation. Wheel
slippage, a common occurrence during movement, leads to accumulated errors in
encoder data. We mitigate this by comparing the IMU-predicted position change
with the encoder data. Discrepancies exceeding a set threshold exclude the
encoder data from the system. IMU data, while relatively accurate in the short
term, suffer from accumulating bias over time. To address this, we compare two
consecutive estimated states to correct for the IMU bias.

Figure 2: Our sensor system is based on a graph.

Our approach leverages a factor graph to represent the relationships between
sensor measurements and robot states (Fig. 2). Each robot state corresponds to
a node in the graph, connected to other states by constraints. These
constraints come in the following forms: LiDAR odometry factor, IMU factor,
and encoder factor. If a sensor exhibits performance degradation, the
corresponding constraint is excluded from the factor graph to maintain
accuracy. Adding constraints to the system is like adding noise to the sensor
measurements. The weight depends on how far the measurements deviate from a
threshold. In case of high repeatability detection from laser data, the
constraint from LiDAR odometry will not be added to the graph.

Assuming the coordinate frames of the LiDAR, IMU, and encoder are aligned with
the robot’s coordinate frame. The robot’s state is expressed as a vector as
shown in equation (1). In this equation, $r$ represents the rotation matrix,
$t$ represents the translation matrix, $v$ represents the velocity matrix, and
b represents the IMU bias.

$x=\begin{bmatrix}r^{T}&t^{T}&v^{T}&b^{T}\end{bmatrix}$ (1)

The raw data of IMU includes the angular velocity and linear acceleration as
shown in equation (2, 3). These measurements are affected by bias $b$ and
noise $n$.

$\omega_{t}=\overline{\omega}_{t}+b_{t}^{\omega}+n_{t}^{\omega}$ (2)

$a_{t}=r_{t}\overline{a}_{t}+b_{t}^{a}+n_{t}^{a}$ (3)

The robot’s state, including its velocity, position, and orientation, is then
estimated by IMU data as follows:

$v_{t+\delta}^{I}=v_{t}+r_{t}^{T}a_{t}\delta$ (4)

$p_{t+\delta}^{i}=p_{t}+v_{t}\delta+\frac{1}{2}r_{t}^{T}at\beta^{2}$ (5)

$r_{t+\delta}^{l}=r_{t}^{T}e^{\omega_{t}^{\delta}}$ (6)

The IMU provides constraint position information between two consecutive
states, which is calculated as follows:

$\Delta_{v}^{i}=r_{t}^{T}\left(v_{t+\delta}-v_{t}\right)$ (7)

$\Delta_{p}^{i}=r_{t}^{T}\left(p_{t+\delta}-p_{t}\right)$ (8)

$\Delta_{r}^{i}=r_{t}^{T}r_{t+\delta}$ (9)

The encoder provides the displacement between two states. The scan matching
step of LiDAR also estimates the displacement of the two states. The position
constraints of the encoder and LiDAR are as follows:

$\Delta_{p}^{0}=r_{t}^{T}\left(p_{t+\delta}-p_{t}\right)$ (10)

$\Delta_{p}^{L}=r_{t}^{T}\left(p_{t+\delta}-p_{t}\right)$ (11)

These constraints are added to the factor graph along with the weights
selected from the sensor degradation evaluation step above. Whenever a new
state and its corresponding constraints are added to the graph, the iSAM2 [15]
optimization method is employed to calculate the most likely robot state based
on all available constraints.

##  3 Experimental Results

The simulated corridor environment was created in Gazebo (Fig. 3(a)). This
environment presented a challenge for 2D LiDAR-based SLAM methods due to the
repetitive nature of corridors, which can lead to drift problems during the
scan-matching process. We defined key distance variables on the map as shown
in Fig. 3(b) to quantify the accuracy of the map.

(a) Environment in Gazebo

(b) Environment with key distances.

Figure 3: Simulation Environment.

To evaluate the performance of different SLAM algorithms, we guided the robot
through a corridor while acquiring sensor data, including LiDAR, IMU, and
encoder readings. Subsequently, we implemented three SLAM algorithms and
assessed their accuracy in generating a map of the environment and tracking
the robot’s trajectory. The accuracy of the map is presented in Table 1, which
demonstrates that our method exhibits reduced robot drift compared to Karto
SLAM when moving in the corridor environment, mapping results by three methods
presented in Fig. 4, and it can be seen that the map from the GMapping
algorithm is very inaccurate. In addition, we observe a partial improvement in
the map deviation. Fig. 5 shows the comparison of the robot’s trajectory
during movement. We utilized the RMSE metric to quantify the accuracy of both
the position and the rotation errors.

Figure 4: Mapping result by (a) GMapping, (b) Karto SLAM, (c) Our method. Table 1: Comparison of Variables and Methods Variable |  True Value |  Karto SLAM |  Our method
---|---|---|---
a |  14.500 |  13.415 |  13.897
b |  21.000 |  19.600 |  20.226
c |  5.000 |  4.863 |  4.908
$\alpha$ |  90.00 |  92.286 |  89.236

Our evaluation compared two established SLAM methods: Gmapping [16] and
KartoSLAM [17]. Gmapping utilizes a particle filter, where each particle
represents a robot state and map. However, in highly repetitive environments,
particles may not update significantly, leading to inaccurate robot pose
estimation and substantial errors. Karto SLAM is a graph-based SLAM technique
that initializes the robot state using odometry data. While subsequent LiDAR
matching refines the pose the reliance on odometry, which is prone to slip and
large rotation angle error can lead to significant errors in the robot’s
directional estimate. Based on graph optimization, our approach uses
additional data from the IMU sensor to improve the estimation of the rotation
angle of the robot by 26% compared to the Karto SLAM as shown in Table 2.
Furthermore, we incorporate odometry data and IMU data to provide additional
constraints, resulting in a more accurate overall estimate of robot state.

Figure 5: Trajectory comparison. Table 2: Comparison of Position and Angle Errors of Different SLAM Methods Method |  Error of position (m) |  Error of angle (degree)
---|---|---
GMapping |  4.5489 |  1.357
Karto SLAM |  0.6032 |  0.923
Our Method |  0.1949 |  0.674

##  4 Conclusion

This paper presented an effective multisensor fusion approach for SLAM in
textureless environments. Our method integrates a sensor selection and
weighting strategy that leverages sensor characteristics to prioritize high-
quality measurements. This combined approach significantly improves the
accuracy of robot positioning and mapping. The factor graph framework enables
flexible adaptation and integration of various sensor types within the system.
Our experimental evaluation demonstrated the ability of our method compared to
Karto SLAM, achieving substantial reductions in both the positioning error
(67. 68%) and the angular error (26. 98%). Future work will focus on
developing a loop closure mechanism, which is crucial for global consistency
in SLAM. In addition, we plan to conduct real-world experiments to validate
the effectiveness of our approach in practical scenarios.

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