# Sub-Terahertz and mmWave Penetration Loss Measurements for Indoor
Environments

Kairui Du, Ozgur Ozdemir, Fatih Erden, and Ismail Guvenc Email: {kdu,
oozdemir, ferden<EMAIL_ADDRESS>Department of Electrical and Computer
Engineering, North Carolina State University, Raleigh, NC

###### Abstract

Millimeter-wave (mmWave) and terahertz (THz) spectrum can support
significantly higher data rates compared to lower frequency bands and hence
are being actively considered for 5G wireless networks and beyond. These bands
have high free-space path loss (FSPL) in line-of-sight (LOS) propagation due
to their shorter wavelength. Moreover, in non-line-of-sight (NLOS) scenario,
these two bands suffer higher penetration loss than lower frequency bands
which could seriously affect the network coverage. It is therefore critical to
study the NLOS penetration loss introduced by different building materials at
mmWave and THz bands, to help establish link budgets for an accurate
performance analysis in indoor environments. In this work, we measured the
penetration loss and the attenuation of several common constructional
materials at mmWave (28 and 39 GHz) and sub-THz (120 and 144 GHz) bands.
Measurements were conducted using a channel sounder based on NI PXI platforms.
Results show that the penetration loss changes extensively based on the
frequency and the material properties, ranging from 0.401 dB for ceiling tile
at 28 GHz, to 16.608 dB for plywood at 144 GHz. Ceiling tile has the lowest
measured attenuation at 28 GHz, while clear glass has the highest attenuation
of 27.633 dB/cm at 144 GHz. As expected, the penetration loss and attenuation
increased with frequency for all the tested materials.

###### Index Terms:

Attenuation, channel sounding, millimeter wave (mmWave), NLOS, penetration
loss, sub-terahertz.

##  I Introduction

In recent years, there has been a rapid increase in the number of wireless
user devices and a surging demand of higher data throughput, making the sub-6
GHz frequency band more congested and incapable of supporting the future data
rate demand. Researchers have thus been motivated to focus on higher
frequencies in the millimeter-wave (mmWave) and terahertz (THz) spectrum.
These higher frequency bands range from 30 GHz to 10 THz, have large amount of
available bandwidth compared to the sub-6 GHz bands, and hence they offer a
promising solution to the increasing data rate demand. For example, IEEE
Communications Society recently identified THz connectivity as one of the nine
communication technology trends to follow [1]. However, as the communication
frequency increases, the wavelength becomes smaller, which significantly
increases the free-space path loss (FSPL) and the penetration loss in mmWave
band and THz bands, both for line-of-sight (LOS) and non-line-of-sight (NLOS)
propagation scenarios.

Propagation and attenuation over common mmWave bands have recently been
studied extensively, following the opening of spectrum above 24 GHz by the FCC
[2]. Reflection and penetration loss measurements at 28 GHz in New York urban
environment [3] showed that the outdoor building materials are good reflectors
with the largest measured reflection coefficient of 0.896 for tinted glass,
while indoor materials were found to be less reflective. A high penetration
loss was observed with the largest to be 45.1 dB for three interior walls of
the office building at 11.39 m separation between the transmitter (Tx) and
receiver (Rx). In [4], the authors found that steerable antennas could help
generate rich number of resolvable multipath components at 28 GHz in both LOS
and NLOS scenarios and thus creating viable links with link distances on the
order of 200 m. Foliage and ground reflection measurements at 73 GHz [5]
showed an average of 0.4 dB/m foliage attenuation, and reflection coefficients
ranged from 0.02 to 0.34 for dirt and gravel ground. The authors in [6]
studied indoor and outdoor penetration loss at 73 GHz and 81 GHz and reported
an average penetration loss of 2 to 9 dB for wood and glass. They also
observed outdoor materials had larger penetration losses. In [7], authors
focused on penetration loss of several typical building materials in three
popular mmWave bands (i.e., 28, 73, 91 GHz). Higher penetration loss was
observed as the communication frequency was increased.

Directional and omnidirectional path loss models are presented in [8], which
developed temporal and spatial channel models and outage probabilities based
on a large number of wideband channel measurements at 28, 38, 60, and 73 GHz.
Another study [9] focused on different theoretical mmWave propagation channel
models to compare LOS propagation, large-scale path loss, and building
penetration loss over the 0.5-100 GHz frequency range. In [10], empirical path
loss models at 60 and 73 GHz were tuned using slope correction factors to
accurately estimate mmWave path loss. In our recent work [11], we introduce
models for power angular-delay profile (PADP) and large-scale path loss for
both LOS and NLOS propagation, based on extensive indoor measurements at 28
GHz. In [12, 13], coverage enhancement for 28 GHz mmWave NLOS propagation
using passive reflector was studied. It was found that the measured received
power with reflectors could approach the received power of FSPL model at the
same travel distance as the NLOS signal.

There are only a limited studies on wireless propagation and penetration at
sub-THz bands, which are expected to be used by the wireless technologies
beyond 5G. An overview in [14] described many technical challenges and
opportunities for wireless communication and sensing applications above 100
GHz and presented new propagation and penetration loss models. In [15], a
multi-ray channel model considering the LOS, reflected, scattered, and
diffracted paths in THz band was given and the THz channel characteristics
were analyzed based on this model. Another study [16] provided deterministic
and statistical channel models in the THz bands and presented hybrid methods,
physical parameters of the THz channel and their implications for wireless
communication design.

Few measurements at THz bands have been conducted so far. Authors in [17]
focused on indoor reflection, penetration, scattering and path loss properties
at both mmWave (28 and 73 GHz) and sub-THz (140 GHz) frequencies. The authors
observed that reflection loss is lower at higher frequencies at a given
incident angle while the penetration loss increases with frequency. Large-
scale indoor path loss models at 140 GHz are provided and revealed a similar
path loss exponent as observed at 28 and 73 GHz. Another study [18] on
penetration loss reported that the loss at the lower end of the THz band is
much lower than the loss at higher frequencies, and that the incident angle
affects the _path length_ inside the material. Undoubtedly, further
measurement results are needed to develop better understanding and modeling of
THz signal propagation.

In this work, we focused on penetration loss measurements of several common
constructional materials, as shown in Fig. 1, including ceiling tile, drywall,
clear glass, and plywood, at both mmWave band (28 and 39 GHz) and sub-THz (120
and 144 GHz) bands. Measurements were carried out using a channel sounder
based on NI’s PXI platform [19] (see Fig. 2), with horn antennas on both Tx
and Rx. We describe the signal generation and reception of our channel sounder
in detail for each of the frequencies in consideration. Both penetration loss
and attenuation were observed to increase with frequency, which were
quantified for different materials. Results show that ceiling tile has the
lowest penetration loss and attenuation at 28 GHz. At 144 GHz, plywood has the
largest penetration loss of 16.068 dB, and clear glass has the highest
attenuation of 27.633 dB/cm.

(a)

(b)

(c)

(d)

Figure 1: The tested constructional materials, namely, (a) ceiling tile, (b)
clear glass, (c) drywall, (d) plywood. Figure 2: Channel sounder block diagram
for the NI PXI platform.

##  II Channel Sounder Setup and Configuration

The block diagram of the channel sounder is given in Fig. 2 [20]. It consists
of NI PXIe-1085 Tx and Rx chassis, Tx and Rx radio heads, and a FS725 Rubidium
(Rb) clock [21]. The PXIe-1085 chasis performs a series of samplings and
conversions as follows [20]. The LabVIEW based sounder code periodically
transmits a Zadoff-Chu (ZC) sequence of length 2048 that is processed by the
root-raised-cosine (RRC) filter. The generated samples are uploaded to the
PXIe-7902 FPGA and are sent to PXIe-3610 digital-to-analog (DAC) converter at
a sampling rate of $f_{s}=3.072$ GS/s. The PXIe-3620 module up-converts the
base-band signal to IF. For the 28 GHz and the 39 GHz setups, the baseband
signal is multiplied with 3 times the first LO signal at $3.52$ GHz, to reach
an IF of $10.56$ GHz. For the 120 GHz and the 144 GHz up-conversion, the IF is
centered at 12 GHz, which is 3 times the LO signal at 4 GHz. Tx radio head
further up-converts the IF signal to RF.

After sounding the channel, the Rx radio head down-converts the RF signal to
IF, and the PXIe-3620 down-convert the IF to baseband. The PXIe-3630 analog-
to-digital converter (ADC) samples the base-band analog signal with a sampling
rate of $f_{s}=3.072$ GS/s. Our channel sounder thus provides $2/f_{s}=0.651$
ns delay resolution in the time domain. Therefore, any multipath component
with a delay higher than $0.651$ ns can be resolved, which represents a path-
length difference of $0.195$ m. The correlation and averaging are performed in
PXIe-7902 FPGA, and the complex channel impulse response (CIR) samples are
sent to the PXIe-8880 host PC for further processing and for saving to local
disk.

The Rb clock is connected to PXIe-6674T modules at both the Tx and the Rx. The
10 MHz signal is used to generate the required local oscillator (LO) signals,
and the transmission at the Tx side and the reception at the RX side were
triggered by the PPS signal. The calibration and the equalization are
performed to eliminate the channel distortion due to the non-idealities of the
hardware itself. Directional horn antennas are later connected to the mmWave
radio heads at the Tx and the Rx sides. Time alignment is finally checked
before the measurement to guarantee an accurate flight time of each peak in
the channel impulse response.

We used different radio heads and horn antennas in penetration measurements at
28, 39, 120, and 144 GHz, as introduced in Section II-A, Section II-B and
Section II-C, respectively. The parameters of the horn antennas are provided
in Table I. The base-band signals are the same for all of the four
frequencies. The bandwidth of the RF signal centered at 28, 39, 120, and 144
GHz is 1.5 GHz regardless of the central frequency. The up-conversion and the
down-conversion process of the radio heads for the corresponding four
frequency bands are provided in Section II-A, Section II-B and Section II-C.

Table I: Horn antenna parameters of 28, 39, and 120/144 GHz. Operating Frequency |  28 GHz |  39 GHz |  120/144 GHz
---|---|---|---
Model |  SAR-1725-34KF-E2 |  SAR-2013-222F-E2 |  VDI WR-6.5
Antenna gain (dBi) |  17 |  20 |  21
3 dB beam width in E plane (degree) |  26 |  15 |  13
3 dB beam width in H plane (degree) |  24 |  16 |  13
Antenna maximum linear dimension (cm) |  4.072 |  4.384 |  1.080
Antenna far-field (cm) |  30.973 |  50.005 |  11.205

###  II-A 28 GHz Tx/Rx Setup

At 28 GHz, NI mmRH-3642 was the Tx radio head and NI mmRH-3652 was the Rx
radio head. The Tx radio head up-converts the IF signal by multiplying 8 times
of the second LO at $4.82$ GHz. The lower side-band is centered at 28 GHz and
the upper side-band is filtered out in the radio head. At the Rx, the Rx radio
head down-converts the RF signal to IF. SAR-1725-34KF-E2 horn antennas are
connected to the Tx and the Rx radio head with 17 dBi gain, 26 degree and 24
degree half power beam-widths in the elevation and the azimuth planes, and a
maximum linear dimension of $4.072$ cm.

###  II-B 39 GHz Tx/Rx Setup

At 39 GHz, NI mmRH-3643 is the Tx radio head and NI mmRH-3653 is the Rx radio
head. The Tx radio head up-converts the IF signal by multiplying 6 times of
the second LO at $4.456$ GHz. The upper side-band is centered at 39 GHz and
the lower side-band is filtered out in the radio head. At the Rx, the Rx radio
head down-converts the RF signal to IF. SAR-2013-222F-E2 horn antennas shown
in Table I are connected to the Tx and the Rx radio head with 20 dBi gain, 15
degree and 16 degree half power beam-width in the elevation and azimuth
planes, and a maximum linear dimension of $4.384$ cm.

Figure 3: Penetration loss measurement setup, with the construction material
located between the Tx and the Rx antennas.

###  II-C 120 GHz and 144 GHz Tx/Rx Setup

At 120 GHz and 144 GHz, VDI WR6.5CCU is used as the Tx radio head and VDI
WR6.5CCD is used as the Rx radio head. The Tx radio head up-converts the IF
signal by multiplying 12 times of the second LO at 9 GHz for 120 GHz, and at
11 GHz for 144 GHz. The upper side-band is centered at 144 GHz and the lower
side-band is filtered out by WR6.5BPFE140-148 bandpass filter, located between
the Tx radio head and the Tx antenna. For the 120 GHz signal, the lower side-
band is filtered out by WR6.5BPFE116-123 bandpass filter. At the Rx, the Rx
radio head down-converts the RF signal to IF. The VDI WR-6.5 horn antennas are
connected to the Tx and the Rx radio head with 21 dBi gain, as shown in Table
I, with 13 degree half power beam-widths in both elevation and azimuth planes,
and a maximum linear dimension of 1.08 cm.

##  III Penetration Loss Measurement Procedure

Table II: List of materials used in the measurement [7]. Material |  Model |  Dimension |  Thickness
---|---|---|---
Ceiling tile |  Armstrong Ceilings Acoustic Panel Ceiling Tiles |  $121.9$ cm $\times$ $60.9$ cm |  $1.13$ cm
Clear glass |  Gardner Glass Products Clear Glass |  $76.2$ cm $\times$ $91.4$ cm |  $0.18$ cm
Drywall |  ToughRock Fireguard Drywall Panel |  $121.9$ cm $\times$ $243.8$ cm |  $1.31$ cm
Plywood (4-ply) |  Plytanium $15/32$ CAT PS1-09 Square Structural Pine Sheathing |  $121.9$ cm $\times$ $243.8$ cm |  $1.12$ cm

The penetration loss measurements of common constructional materials were
conducted in an indoor environment in Engineering Building 2 at NC State
University, Raleigh, NC. List of the materials used for the penetration loss
measurements is given in Table II, along with their dimensions and models.
Fig. 3 illustrates the measurement scenario. The Tx and the Rx were first
aligned to each other, and the LOS received power without blockage was
measured. Then, the material was introduced in the center of the Tx and the
Rx, and was further aligned to both Tx and Rx so that Tx and Rx were pointing
directly to the material at 0 degree incident angle. The NLOS received power
with the blockage was then measured. After all the received power was measured
with different materials’ blockage, both the Tx and the Rx were moved to the
next position and we repeated the measurement procedure mentioned above.

For the 28 GHz and the 39 GHz measurements, a maximum distance of 80 cm from
the Tx and the Rx to the material was chosen, thus the cross-section of the
material and the antenna main lobe would be much smaller than the dimensions
of the material [7], and the effect of diffraction and the edge scattering was
minimized. For the 120 GHz and 144 GHz measurements, the maximum distance was
chosen as 70 cm due to the length limit of the desk that held the materials
and the radio heads, as shown in Fig. 4. The minimal distance to the materials
was chosen according to the far field region $R$ of the horn antennas, which
is calculated as:

$\displaystyle\mathrm{R}>\frac{2D^{2}}{\lambda}\leavevmode\nobreak\
,\quad\mathrm{R}\gg D\leavevmode\nobreak\
,\quad\mathrm{R}\gg\lambda\leavevmode\nobreak\ ,$ (1)

where $\lambda$ is the wave length of the radiated signal and $D$ is the
maximum linear dimension of the antenna. We make sure that the materials are
in the far field region of both the Tx and the Rx antenna because in this
region radiated fields dominate, and the radiation pattern does not change
shape with distance.

Figure 4: 120 GHz and 144 GHz measurements setup.

The calculated far fields for the three different antennas are shown in Table
I. The 28 GHz antennas have far field region greater than 30 cm. Therefore,
the received power with and without blockage was measured when the material is
30 cm to 80 cm away from both the Tx and the Rx, with a resolution of 10 cm.
The 39 GHz antennas have far field region greater than 50 cm, and therefore we
measured the received power with and without blockage when the material is 50
cm to 80 cm away from both the Tx and the Rx with 10 cm resolution. The far
field region of the 120 GHz and the 144 GHz antennas are greater than 11 cm,
and hence, the received power with and without blockage was measured when the
material is 20 to 70 cm away from the Tx and the Rx, with 10 cm resolution.
Transmit power was set to -10 dBm for all the measurements to protect the
receiver at close distances.

The received power with blockage $P_{r,{\textrm{LOS}}}$ and without blockage
$P_{r,{\textrm{blocked}}}$ can be calculated as:

$\displaystyle\mathrm{P}_{r,{\textrm{LOS}}}\leavevmode\nobreak\ ({\rm dB})$
$\displaystyle=P_{t}+G_{t}+G_{r}-\rm FSPL\leavevmode\nobreak\ ,$
$\displaystyle\mathrm{P}_{r,{\textrm{blocked}}}\leavevmode\nobreak\ ({\rm
dB})$ $\displaystyle=P_{t}+G_{t}+G_{r}-\rm
FSPL-\mathrm{Penetration\leavevmode\nobreak\ Loss},$

where $P_{t}$ is the transmitted power, $G_{t}$ and $G_{r}$ are the Tx and the
Rx antenna gain, FSPL is the free space path loss which is the same for both
cases since the signals travel the same distances.

Therefore, the penetration loss can be further derived from the measured LOS
power without blockage $P_{r,{\textrm{LOS}}}$ and the measured blocked LOS
received power $P_{r,{\textrm{blocked}}}$ at the same Tx and Rx separation,
using:

$\mathrm{Penetration\leavevmode\nobreak\ Loss\leavevmode\nobreak\ (\rm
dB)}=P_{r,{\textrm{LOS}}}-P_{r,{\textrm{blocked}}}\leavevmode\nobreak\ .$ (2)

(a)

(b)

Figure 5: Measurement (a) without blockage, (b) with material blockage.

Fig. 5(a) and Fig. 5(b) illustrate an example measurement setup for the LOS
case and the blocked LOS case, respectively, for the 144 GHz measurements.
Note that the Tx and the Rx radio heads were placed above the ground high
enough so that in the unblocked scenario the ground reflection is resolvable
to the LOS component at close measured distance. At larger distance, the
ground reflection is not resolvable to the LOS component, but its effect is
minimized by the narrow beam of our antennas. Received power was directly read
from the first arriving multipath component in the CIR. To get a more static
and accurate result, the CIR in each measurement was averaged over 32 scans by
the sounder code.

##  IV Measurement Results and Analysis

Table III: Measurement results of average received power, penetration loss, standard deviation of penetration loss, and attenuation at 28 GHz, 39 GHz, 120 GHz, and 140 GHz for ceiling tile, clear glass, drywall, and plywood. Material | Frequency |  $P_{r,{\textrm{LOS}}}$ (dBm) |  $P_{r,{\textrm{blocked}}}$ (dBm) | Penetration Loss (dB) | Standard Deviation (dB) | Attenuation (dB/cm)
---|---|---|---|---|---|---
Ceiling tile | 28 GHz | $-37.722$ | $-38.123$ | $0.401$ | $0.027$ | $0.355$
39 GHz | $-39.005$ | $-39.853$ | $0.848$ | $0.083$ | $0.75$
120 GHz | $-38.279$ | $-40.993$ | $2.714$ | $0.269$ | $2.402$
144 GHz | $-39.405$ | $-43.524$ | $4.119$ | $0.925$ | $3.645$
Clear glass | 28 GHz | $-37.722$ | $-38.513$ | $0.791$ | $0.009$ | $4.394$
39 GHz | $-39.005$ | $-42.777$ | $3.772$ | $0.087$ | $20.956$
120 GHz | $-38.279$ | $-43.007$ | $4.728$ | $0.083$ | $26.267$
144 GHz | $-39.405$ | $-44.379$ | $4.974$ | $0.786$ | $27.633$
Drywall | 28 GHz | $-37.722$ | $-38.858$ | $1.137$ | $0.037$ | $0.868$
39 GHz | $-39.005$ | $-40.503$ | $1.498$ | $0.103$ | $1.144$
120 GHz | $-38.279$ | $-41.196$ | $2.917$ | $1.641$ | $2.227$
144 GHz | $-39.405$ | $-43.193$ | $3.788$ | $2.789$ | $2.892$
Plywood | 28 GHz | $-37.722$ | $-40.838$ | $3.116$ | $0.934$ | $2.782$
39 GHz |  -$39.005$ | $-43.274$ | $4.269$ | $0.597$ | $3.812$
120 GHz | $-38.279$ | $-52.616$ | $14.337$ | $4.276$ | $12.801$
144 GHz | $-39.405$ | $-55.473$ | $16.068$ | $3.845$ | $14.346$

The measurement results were averaged over all the measured positions. The
averaged received power, penetration loss, standard deviation for the
penetration loss, and attenuation for different materials at 28 GHz, 39 GHz,
120 GHz, and 144 GHz are provided in Table III. The averaged received power of
the LOS path (at the same travel distance as the blocked case) of all the
measured positions is denoted by $P_{r,{\textrm{LOS}}}$. On the other hand,
$P_{r,{\textrm{blocked}}}$ is the averaged received power of the NLOS ray that
is blocked by the materials. Penetration loss was calculated from (2) based on
the difference of the received power with and without blockage. The standard
deviation indicated the variation of the calculated penetration loss. The
attenuation in dB/cm, which represents the penetration loss of unit thickness
of the material, is the averaged penetration loss over material thickness.

As shown in Table III, the lowest penetration loss was measured as $0.401$ dB
for ceiling tile at 28 GHz and the highest was $16.068$ dB at 144 GHz. At all
four frequencies, ceiling tile has the lowest penetration loss ranging from
$0.401$ dB at 28 GHz to $4.119$ dB at 144 GHz among all the materials, while
plywood has the largest penetration loss ranging from $3.116$ dB at 28 GHz to
$16.068$ dB at 144 GHz. On the other hand, the attenuation of clear glass is
the highest compared with other materials at each frequencies. A largest
attenuation of $27.633$ dB/cm was observed at 144 GHz for clear glass. At 28
GHz and 39 GHz, the standard deviation of the penetration loss for all the
materials was all less than 1 dB. However, for 120 and 144 GHz the standard
deviation increased, with a maximum of $4.276$ dB for plywood at 120 GHz.
Plywood has the largest standard deviation at all frequencies, which could
somehow be explained by the diffuse reflection at the rough surface of the
plywood. Besides, as wavelength gets smaller, the surface of the material is
rougher for the incident ray, thus causing an increased variation in
penetration loss at higher frequencies.

The averaged penetration loss and attenuation of different materials at four
different frequencies were plotted in Fig. 6. The overall results show that
the penetration loss and the attenuation increases with frequency. Fig. 6(a)
indicates that plywood has an attenuation larger than 14 dB, which would
seriously degrade the performance of 120 GHz and 144 GHz NLOS signal
propagation when penetrating through walls and floors, while all the other
materials have attenuation less than 5 dB at all frequencies. Fig. 6(b) shows
the effect of material thickness. Although the penetration loss of clear glass
board was less than 5 dB, the attenuation was larger than 20 dB/cm at 39 GHz,
120 GHz, and 144 GHz. A thin glass window or wall is therefore necessary for
better outdoor to indoor coverage at these three bands.

(a)

(b)

Figure 6: The averaged results of (a) penetration loss, (b) attenuation for
ceiling tile, clear glass, drywall, and plywood at 28, 39, 120, and 144 GHz.

##  V Conclusion

In this work, we measured the penetration loss of several common
constructional materials at 28 GHz, 39 GHz, 120 GHz, and 144 GHz. The maximum
distance from the Tx and the Rx to the materials was chosen to eliminate the
edge scattering effect. The minimal distance from the Tx and the Rx to the
materials was calculated to ensure both the Tx and the Rx antennas were in the
far field region. Ground reflection was minimized by using narrow beam
antennas. The measured constructional materials were ceiling tile, glass,
drywall, and plywood. The penetration loss results, after being averaged over
all the measured positions, ranged from $0.401$ dB for ceiling tile at 28 GHz
to $16.068$ dB for plywood at 144 GHz. The highest attenuation of $27.633$
dB/cm was observed for clear glass at 144 GHz. Overall, the penetration loss
and attenuation increases with frequency for all the materials. These results
could be helpful for developing mmWave and THz channel models that accurately
estimate the penetration loss of common building materials. They can further
contribute to link budget calculation for future 5G/6G deployments in indoor
environments and for developing accurate penetration models for ray-tracing
simulations.

## Acknowledgement

This work was supported in part by NASA under the Award ID NNX17AJ94A, and in
part by DOCOMO Innovations, Inc.

## References

  * [1] The CTN Editorial Board, “Nine Communications Technology Trends for 2020,” Technical report, accessed: 1-22-2020. [Online]. Available: https://www.comsoc.org/publications/ctn/nine-communications-technology-trends-2020
  * [2] C. Meisch, “FCC adopts rules to facilitate next generation wireless technologies,” Technical report, accessed: 3-30-2019. [Online]. Available: https://www.fcc.gov/document/fcc-adopts-rules-facilitate-next-generation-wireless-technologies
  * [3] H. Zhao, R. Mayzus, S. Sun, M. Samimi, J. K. Schulz, Y. Azar, K. Wang, G. N. Wong, F. Gutierrez, and T. S. Rappaport, “28 GHz millimeter wave cellular communication measurements for reflection and penetration loss in and around buildings in New York city,” in _Proc. IEEE Int. Conf. Commun. (ICC)_ , Budapest, Hungary, June 2013, pp. 5163–5167.
  * [4] Y. Azar, G. N. Wong, K. Wang, R. Mayzus, J. K. Schulz, H. Zhao, F. Gutierrez, D. Hwang, and T. S. Rappaport, “28 GHz propagation measurements for outdoor cellular communications using steerable beam antennas in New York city,” in _Proc. IEEE Int. Conf. Commun. (ICC)_ , Budapest, Hungary, June 2013, pp. 5143–5147.
  * [5] T. S. Rappaport and S. Deng, “73 GHz wideband millimeter-wave foliage and ground reflection measurements and models,” in _Proc. IEEE Int. Conf. Commun. (ICC)_ , London, UK, June 2015, pp. 1238–1243.
  * [6] M. Khatun, C. Guo, D. Matolak, and H. Mehrpouyan, “Indoor and outdoor penetration loss measurements at 73 and 81 GHz,” _arXiv preprint arXiv:1908.00166_ , 2019.
  * [7] N. Hosseini, M. Khatun, C. Guo, K. Du, O. Ozdemir, D. W. Matolak, I. Guvenc, and H. Mehrpouyan, “Attenuation of several common building materials in millimeter-wave frequency bands: 28, 73 and 91 GHz,” _arXiv preprint arXiv:2004.12568_ , 2020.
  * [8] T. S. Rappaport, G. R. MacCartney, M. K. Samimi, and S. Sun, “Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design,” _IEEE Trans. Commun._ , vol. 63, no. 9, pp. 3029–3056, Sept. 2015.
  * [9] T. S. Rappaport, Y. Xing, G. R. MacCartney, A. F. Molisch, E. Mellios, and J. Zhang, “Overview of millimeter wave communications for fifth-generation (5G) wireless networks—with a focus on propagation models,” _IEEE Trans. Antennas Propag._ , vol. 65, no. 12, pp. 6213–6230, Dec. 2017.
  * [10] A. I. Sulyman, A. Alwarafy, G. R. MacCartney, T. S. Rappaport, and A. Alsanie, “Directional radio propagation path loss models for millimeter-wave wireless networks in the 28, 60, and 73 GHz bands,” _IEEE Trans. Wireless Commun._ , vol. 15, no. 10, pp. 6939–6947, Oct. 2016\.
  * [11] F. Erden, O. Ozdemir, and I. Guvenc, “28 GHz mmWave channel measurements and modeling in a library environment,” in _Proc. IEEE Radio Wireless Symp. (RWS)_ , San Antonio, TX, Jan. 2020, pp. 52–55.
  * [12] W. Khawaja, O. Ozdemir, Y. Yapici, I. Guvenc, and Y. Kakishima, “Coverage enhancement for mmWave communications using passive reflectors,” in _Proc. Global Symp. Millimeter Waves (GSMM)_ , Boulder, CO, May 2018, pp. 1–6.
  * [13] W. Khawaja, O. Ozdemir, F. Erden, I. Guvenc, M. Ezuma, and Y. Kakishima, “Effect of passive reflectors for enhancing coverage of 28 GHz mmWave systems in an outdoor setting,” in _Proc. IEEE Radio Wireless Symp. (RWS)_ , Orlando, FL, Jan. 2019, pp. 1–4.
  * [14] T. S. Rappaport, Y. Xing, O. Kanhere, S. Ju, A. Madanayake, S. Mandal, A. Alkhateeb, and G. C. Trichopoulos, “Wireless communications and applications above 100 GHz: Opportunities and challenges for 6G and beyond,” _IEEE Access_ , vol. 7, pp. 78 729–78 757, June 2019\.
  * [15] C. Han, A. O. Bicen, and I. F. Akyildiz, “Multi-ray channel modeling and wideband characterization for wireless communications in the terahertz band,” _IEEE Trans. Antennas Propag._ , vol. 14, no. 5, pp. 2402–2412, May 2015.
  * [16] C. Han and Y. Chen, “Propagation modeling for wireless communications in the terahertz band,” _IEEE Commun. Mag._ , vol. 56, no. 6, pp. 96–101, Jun. 2018.
  * [17] Y. Xing, O. Kanhere, S. Ju, and T. S. Rappaport, “Indoor wireless channel properties at millimeter wave and sub-terahertz frequencies,” in _Proc. IEEE Global Commun. Conf. (GLOBECOM)_ , Waikoloa, HI, Dec. 2019, pp. 1–6.
  * [18] J. Kokkoniemi, J. Lehtomäki, V. Petrov, D. Moltchanov, and M. Juntti, “Frequency domain penetration loss in the terahertz band,” in _Proc. Global Symp. Millimeter Waves (GSMM)_ , Espoo, Finland, Jun. 2016, pp. 1–4.
  * [19] NI, “mmWave Transceiver System,” accessed: 7-31-2018. [Online]. Available: http://www.ni.com/sdr/mmwave
  * [20] F. Erden, O. Ozdemir, W. Khawaja, and I. Guvenc, “Correction of channel sounding clock drift and antenna rotation effects for mmWave angular profile measurements,” _IEEE Open J. Ant. Propag._ , vol. 1, pp. 71–87, 2020\.
  * [21] Standford Research Systems, “FS725 Rubidium Frequency Standard,” accessed: 7-31-2018. [Online]. Available: https://www.thinksrs.com/products/fs725.html


# Temporal Waypoint Navigation of Multi-UAV Payload System using Barrier
Functions

Nishanth Rao1, Suresh Sundaram1,2, and Pushpak Jagtap2 1Pushpak Jagtap is with
the Robert Bosch Center for Cyber-Physical Systems, Nishanth Rao is with the
Department of Aerospace Engineering, and Suresh Sundaram is with the Robert
Bosch Center for Cyber-Physical Systems and the Department of Aerospace
Engineering at Indian Institute of Science, Bangalore, India
<EMAIL_ADDRESS>
###### Abstract

Aerial package transportation often requires complex spatial and temporal
specifications to be satisfied in order to ensure safe and timely delivery
from one point to another. It is usually efficient to transport versatile
payloads using multiple UAVs that can work collaboratively to achieve the
desired task. The complex temporal specifications can be handled coherently by
applying Signal Temporal Logic (STL) to dynamical systems. This paper
addresses the problem of waypoint navigation of a multi-UAV payload system
under temporal specifications using higher-order time-varying control barrier
functions (HOCBFs). The complex nonlinear system of relative degree two is
transformed into a simple linear system using input-output feedback
linearization. An optimization-based control law is then derived to achieve
the temporal waypoint navigation of the payload. The controller’s efficacy and
real-time implementability are demonstrated by simulating a package delivery
scenario inside a high-fidelity Gazebo simulation environment.

##  I Introduction

Advancements in multi-UAV system research and technologies have led to the
widespread use of multi-UAV systems in the aerial transportation of payloads
from one point to another. It is evident that using multiple UAVs to deliver
versatile payloads is more efficient than utilizing a single UAV of varying
lift capacities. In addition, payloads need to be delivered to specific
locations under some time constraints. For example, in the air delivery of
packages, it is crucial to not only deliver the package at the correct
location, but the package must also reach within the specified time. Thus it
is essential to design control algorithms for multi-UAV payload systems that
follow certain temporal specifications while enabling safe payload
transportation.

Most of the literature focuses on developing trajectory-tracking controllers
for multi-UAV payloads without considering temporal specifications. In [1],
the authors propose a trajectory tracking controller using geometric control
for a UAV fleet carrying the payload using cable suspension. In [2], a
distributed model predictive control algorithm is developed for the purpose of
trajectory tracking of payload using rigid link payload suspension. The
authors in [3] develop an adaptive controller for a cable-suspended payload
with user-specified safety constraints. For a rigid link suspended payload, a
feedback linearized nonlinear controller is presented in [4].

Tasks that require complex spatial and temporal requirements can be handled
effectively by applying Signal Temporal Logic (STL) [5] to dynamical systems.
The authors in [6] use control barrier functions [7, 8] to design control
inputs enforcing a class of STL specifications. In [9], a dynamically feasible
STL-based planning and control algorithm is designed for a single UAV system
that satisfies complex spatial and temporal requirements. An extension to
multi-UAV fleets (without payload) is proposed in [10] that generates
continuous trajectories for multiple UAVs to meet the temporal requirements.

While there have been works on designing controllers for multi-agent systems
to satisfy STL specifications [11], there has been no work on developing
controllers to satisfy complex STL specifications, particularly for a multi-
UAV system carrying a payload. One of the reasons is that the dynamics of such
a system is highly coupled and nonlinear in nature. This can lead to a complex
state-space representation with large state and control vector dimensions. The
curse of dimensionality can thus make it difficult to control such a system
under STL specifications.

This paper focuses on developing a controller for the multi-UAV payload system
to enforce the complex STL specifications using Higher-Order Time-Varying
Control Barrier Functions (HOCBFs). The model complexity of the system is
reduced by the application of input-output feedback linearization, which
results in a linear system with a relative degree equal to 2. The STL
specifications are captured using time-varying HOCBFs, and an optimization-
based control law is proposed. To validate the efficacy and real-time
implementability of the proposed controller, a simulation environment is
developed using the Gazebo simulator for the purpose of simulating a package
delivery scenario under time specifications.

Section II discusses the necessary preliminaries and notations used in this
paper. Section III proposes a control law for temporal waypoint navigation of
the multi-UAV payload system. In Section IV, the proposed control law is
validated in a high-fidelity Gazebo simulator that simulates a package-
delivery scenario. Section V concludes the proposed work.

##  II Preliminaries

In this paper, scalars and vectors are denoted by non-bold letters $a$,
whereas matrices are denoted by bold letters $\boldsymbol{A}$. We use
$\mathbb{R}$, $\mathbb{R}^{+}$, and $\mathbb{R}^{+}_{0}$ to denote real,
positive real, and nonnegative real numbers, respectively. $\mathbb{R}^{n}$
denotes an $n$-dimensional vector with real elements and $\mathbb{R}^{m\times
n}$ denotes an $m\times n$ matrix with real elements. The vector
$\mathbb{k}=\left[0\ 0\ 1\right]^{T}\in\mathbb{R}^{3}$ represents the unit
$z$-axis. The matrix $\boldsymbol{I}_{n}\in\mathbb{R}^{n\times n}$ denotes the
$n\times n$ identity matrix. The Moore-Penrose pseudoinverse of a general
matrix $A\in\mathbb{R}^{m\times n}$ is denoted by
$A^{\dagger}\in\mathbb{R}^{n\times m}$. A real-valued $n$-dimensional signal
is denoted by $x:\mathbb{R}^{+}_{0}\rightarrow\mathbb{R}^{n}$. The notation
$x$ is abused by also referring to the trajectory of a dynamical system with
$n$ states. Thus, the meaning of $x$ is assumed to be clear from the context.
A function $\alpha:\mathbb{R}_{0}^{+}\rightarrow\mathbb{R}_{0}^{+}$ is a class
$\mathcal{K}$ function if it is continuous and strictly increasing, with
$\alpha(0)=0$. The lie derivative of a vector field $b$ along the vector field
$a$ is denoted by $\mathcal{L}_{a}b=a\cdot\frac{\partial b}{\partial x}$. The
function composition operator $\circ$ is defined as $f\circ g=f(g(.))$.

###  II-A Payload-UAV System Description

There are, in general, $N$ UAVs connected to the rigid massless rods, each of
length $l_{i}$ via spherical joints. These rods are rigidly connected to the
payload and thus always remain vertical. The location of the center of mass of
the payload and the $i^{th}$ UAV is denoted by $r_{0}\in\mathbb{R}^{3}$ and
$r_{i}\in\mathbb{R}^{3}$ respectively. The vector $\rho_{i}\in\mathbb{R}^{3}$
denotes the position of the attachment between the rod corresponding to the
$i^{th}$ UAV and the payload with respect to the center of mass of the
payload. The mass of the payload and the $i^{th}$ UAV is denoted by
$m_{0},m_{i}\in\mathbb{R}^{+}$ respectively. The inertia matrix of the payload
and the $i^{th}$ UAV is indicated by
$\boldsymbol{J}_{0},\boldsymbol{J}_{i}\in\mathbb{R}^{3\times 3}$ respectively.
The rotation matrix $\boldsymbol{R}_{0}\in SO(3)$ and $\boldsymbol{R}_{i}\in
SO(3)$ denotes the orientation of the payload and the $i^{th}$ UAV
respectively. This rotation matrix converts a vector in the body-fixed frame
to the inertial frame. The payload-UAV system is modelled in the standard
North, East and Down frame (NED), with the positive unit $z$-axis pointing
downwards. The total thrust force produced by all the motors of the $i^{th}$
UAV is denoted by $F_{t_{i}}\in\mathbb{R}^{+}$ and is related to the force
vector $F_{i}\in\mathbb{R}^{3}$ as
$F_{i}=F_{t_{i}}\boldsymbol{R}_{i}\mathbb{k}$. The motors produce a torque
vector in the body frame of the $i^{th}$ UAV denoted by
$\tau_{i}=\left[\tau_{x_{i}}\ \tau_{y_{i}}\
\tau_{z_{i}}\right]^{T}\in\mathbb{R}^{3}$. Thus, the overall control input for
the multi-UAV system is $\\{F_{t_{i}},\tau_{i}\\}$ with
$i=\left\\{1,\ldots,N\right\\}$.

###  II-B Payload-UAV Dynamics and State-space Representation

Using the description of the payload-UAV system discussed in Section II-A, the
equations of motion for the multi-UAV payload system (shown in Fig. 1) can be
derived. As the rigid links are always vertical, the position of the $i^{th}$
UAV can be inferred as:

$\displaystyle
r_{i}=r_{0}+\boldsymbol{R}_{0}\left(\rho_{i}-l_{i}\mathbb{k}\right).$ (1)

The kinematic equations are given by:

$\displaystyle\dot{r}_{0}$ $\displaystyle=\boldsymbol{R}_{0}v_{0},$ (2)
$\displaystyle\dot{\boldsymbol{R}}_{0}$
$\displaystyle=\boldsymbol{R}_{0}\omega_{0}^{\times},$ (3)
$\displaystyle\dot{r}_{i}$
$\displaystyle=\dot{r}_{0}+\boldsymbol{R}_{0}\omega_{0}^{\times}\left(\rho_{i}-l_{i}\mathbb{k}\right),$
(4) $\displaystyle\dot{\boldsymbol{R}}_{i}$
$\displaystyle=\boldsymbol{R}_{i}\omega_{i}^{\times},$ (5)

where the skew-symmetric operator $(\cdot)^{\times}:\mathbb{R}^{3}\rightarrow
SO(3)$ denotes the hat map which maps a vector to a skew-symmetric matrix,
$v_{0}\in\mathbb{R}^{3}$ denotes the linear velocity of the payload in the
payload-fixed frame, $\omega_{0}\in\mathbb{R}^{3}$ and
$\omega_{i}\in\mathbb{R}^{3}$ denotes the angular velocities of the payload
and the $i^{th}$ UAV, respectively.

$r_{0},\ \boldsymbol{R}_{0}$$r_{i},\
\boldsymbol{R}_{i}$$\rho_{i}$xyz$f_{i}$$l_{i}$ Figure 1: A schematic diagram
illustrating the payload transport using multiple UAVs. The support-frame
together with the payload (shown lightly as a black cylinder) is modelled as a
cuboid.

Using the Lagrangian formulation and the Lagrange-d’Alembert Principle, one
can arrive at the payload-UAV system dynamics:

$\displaystyle\begin{split}m_{T}\left(\dot{v}_{0}+\omega_{0}^{\times}v_{0}\right)+\sum_{i=1}^{N}m_{i}\left(-\rho_{i}^{\times}\dot{\omega}_{0}+\left(\omega_{0}^{\times}\right)^{2}\rho_{i}\right)\\\
=\boldsymbol{R}_{0}^{T}\left(m_{T}g\mathbb{k}+\sum_{i=1}^{N}F_{i}\right),\ \ \
\ \ \ \end{split}$ (6)
$\displaystyle\begin{split}\sum_{i=1}^{N}m_{i}\rho_{i}^{\times}\left(\dot{v}_{0}+\omega_{0}^{\times}v_{0}\right)+\boldsymbol{\bar{J}}_{0}\dot{\omega}_{0}+\omega_{0}^{\times}\boldsymbol{\bar{J}}_{0}\omega_{0}\\\
=\sum_{i=1}^{N}\rho_{i}^{\times}\boldsymbol{R}_{0}^{T}\left(F_{i}+m_{i}g\mathbb{k}\right),\
\ \ \ \ \end{split}$ (7)
$\displaystyle\begin{split}\boldsymbol{J}_{i}\dot{\omega}_{i}+\omega_{i}^{\times}\boldsymbol{J}\omega_{i}=\tau_{i},\end{split}$
(8)

where the quantity $m_{T}=m_{0}+\sum_{i=1}^{N}m_{i}$ is the total combined
mass, and
$\boldsymbol{\bar{J}}_{0}=\left(\boldsymbol{J}_{0}-\sum_{i=1}^{N}m_{i}\left(\rho_{i}^{\times}\right)^{2}\right)$
is the apparent moment of inertia of the payload. For a detailed derivation,
please refer to [4]. In order to obtain a state-space representation of the
payload-UAV dynamic model, define the state vector as:

$\displaystyle x=\left[\underbrace{r_{0}^{T}\ v_{0}^{T}\ \Theta_{0}^{T}\
\omega_{0}^{T}}_{\text{payload
$\in\mathbb{R}^{12}$}}\underbrace{\Theta_{i}^{T}\
\omega_{i}^{T}}_{\text{$i^{th}$ UAV $\in\mathbb{R}^{6}$}}\right]^{T},\
i\in\\{1,...,N\\},$ (9)

where $\Theta_{0},\Theta_{i}\in\mathbb{R}^{3}$ are the $ZYX$ Euler angle
characterization of the attitudes $\boldsymbol{R}_{0},\boldsymbol{R}_{i}$
respectively. The nonlinear state-space equations can be obtained in the form
$\dot{x}=f\left(x,u\right)$ by rearranging (2) - (8), where the control input
to the system is $u=\left[F_{t_{i}}\ \tau_{x_{i}}\ \tau_{y_{i}}\
\tau_{z_{i}}\right]^{T}\in\mathbb{R}^{4N},\ i=1,\ldots,N$ and are given below
(in addition to the kinematic equations of (2) - (5)):

$\begin{bmatrix}\dot{v}_{0}\\\
\dot{\omega}_{0}\end{bmatrix}=\boldsymbol{\zeta}\times\boldsymbol{\xi},$ (10)

where $\boldsymbol{\zeta}\in\mathbb{R}^{6\times 6}$,
$\boldsymbol{\xi}\in\mathbb{R}^{6\times 1}$ and are given as follows:

$\boldsymbol{\zeta}=\left[\begin{array}[]{c|c}m_{T}\boldsymbol{I}_{3}&-\sum_{i=1}^{N}m_{i}\rho_{i}^{\times}\\\
\hline\cr\sum_{i=1}^{N}m_{i}\rho_{i}^{\times}&\boldsymbol{\bar{J}}_{0}\end{array}\right]^{-1}=\left[\begin{array}[]{c|c}\boldsymbol{P}_{11}&\boldsymbol{P}_{12}\\\
\hline\cr\boldsymbol{P}_{21}&\boldsymbol{P}_{22}\end{array}\right]$ (11)
$\boldsymbol{\xi}=\leavevmode\resizebox{436.8687pt}{}{$\left[\begin{array}[]{c}-m_{T}\omega_{0}^{\times}v_{0}-\sum_{i=1}^{N}m_{i}\left(\omega_{0}^{\times}\right)^{2}\rho_{i}+m_{T}g\boldsymbol{R}_{0}^{T}\mathbb{k}+\sum_{i=1}^{N}\boldsymbol{R}_{0}^{T}F_{i}\\\
\hline\cr-\omega_{0}^{\times}\bar{\boldsymbol{J}}_{0}\omega_{0}-\sum_{i=1}^{N}m_{i}\rho_{i}^{\times}\omega_{0}^{\times}v_{0}+\sum_{i=1}^{N}\rho_{i}^{\times}\boldsymbol{R}_{0}^{T}\left(F_{i}+m_{i}g\mathbb{k}\right)\end{array}\right]$}$
(12)

In order to simplify the complexity of the system dynamics, the input-output
feedback linearization can be applied to the translational dynamics of the
payload. Consider the output of the system to be the position of the payload,
i.e., $y=r_{0}$. The relative degree $\eta$ of the system is 2, since the
control input appears in $\dot{v}_{0}$ as seen in (10). Thus, one has to
differentiate $r_{0}$ twice to obtain the control inputs explicitly:

$\displaystyle\dot{r}_{0}$ $\displaystyle=\boldsymbol{R}_{0}v_{0},$ (13)
$\displaystyle\ddot{r}_{0}$
$\displaystyle=\dot{\boldsymbol{R}}_{0}v_{0}+\boldsymbol{R}_{0}\dot{v}_{0},$
(14)

where $\dot{v}_{0}$ is expanded from (10) as:

$\displaystyle\begin{split}\dot{v}_{0}&=\boldsymbol{P}_{11}\left(-m_{T}\omega_{0}^{\times}v_{0}-\sum_{i=1}^{N}m_{i}\left(\omega_{0}^{\times}\right)^{2}\rho_{i}+m_{T}g\boldsymbol{R}_{0}^{T}\mathbb{k}\right)\\\
&+\underbrace{\boldsymbol{P}_{12}\left(-\omega_{0}^{\times}\bar{\boldsymbol{J}}_{0}\omega_{0}-\sum_{i=1}^{N}m_{i}\rho_{i}^{\times}\omega_{0}^{\times}v_{0}+\sum_{i=1}^{N}\rho_{i}^{\times}\boldsymbol{R}_{0}^{T}m_{i}g\mathbb{k}\right)}_{\text{a
function of state $\overline{f(x)}$}}\\\
&+\underbrace{\boldsymbol{P}_{11}\sum_{i=1}^{N}\boldsymbol{R}_{0}^{T}F_{i}+\boldsymbol{P}_{12}\sum_{i=1}^{N}\rho_{i}^{\times}\boldsymbol{R}_{0}^{T}F_{i}}_{\text{a
function of state and control input}}\end{split}$ (15)

which can be simplified to:

$\displaystyle\dot{v}_{0}$
$\displaystyle=\overline{f(x)}+\left(\boldsymbol{P}_{11}\boldsymbol{S}_{1}+\boldsymbol{P}_{12}\boldsymbol{S}_{2}\right)\overline{\mathbb{u}},$
(16)

where $\boldsymbol{S}_{1}=\left[\boldsymbol{I}_{3}\ \ldots\
\boldsymbol{I}_{3}\right]\in\boldsymbol{R}^{3\times 3N}$,
$\boldsymbol{S}_{2}=\left[\rho_{1}^{\times}\ \ldots\
\rho_{N}^{\times}\right]\in\boldsymbol{R}^{3\times 3N}$, and
$\overline{\mathbb{u}}=\left[\mathbb{u}_{1}^{T}\ \cdots\
\mathbb{u}_{N}^{T}\right]\in\mathbb{R}^{3N}$ with
$\mathbb{u}_{i}=\boldsymbol{R}^{T}_{0}F_{i}$. Substituting (16) in (14)
yields:

$\displaystyle\ddot{r}_{0}$
$\displaystyle=\underbrace{\boldsymbol{R}_{0}\omega_{0}^{\times}v_{0}+\boldsymbol{R}_{0}\overline{f(x)}}_{\text{$d(x)$}}+\underbrace{\boldsymbol{R}_{0}\left(\boldsymbol{P}_{11}\boldsymbol{S}_{1}+\boldsymbol{P}_{12}\boldsymbol{S}_{2}\right)}_{\text{$\Delta(x)$}}\bar{\mathbb{u}}.$
(17)

Let $\overline{\mathbb{u}}=\Delta^{\dagger}(x)\mathbb{v}-d(x)$. Then, (17)
simplifies to

$\displaystyle\boxed{\ddot{y}=\ddot{r}_{0}=\left[\begin{array}[]{l}\ddot{r}_{0_{x}}\\\
\ddot{r}_{0_{y}}\\\
\ddot{r}_{0_{z}}\end{array}\right]=\left[\begin{array}[]{l}\mathbb{v}_{1}\\\
\mathbb{v}_{2}\\\ \mathbb{v}_{3}\end{array}\right]=\mathbb{v}.}$ (24)

Thus, the feedback linearized dynamics of (24) is a fairly simple linear
system which is more conducive to the design of STL-based controllers. A more
rigorous procedure of feedback linearization process for the multi-UAV payload
system can be found in [4].

###  II-C Signal Temporal Logic (STL)

Signal Temporal Logic (STL) [5] provides a formal framework to capture high-
level specifications that can handle spatial, temporal, and logical
constraints. It consists of a set of predicates $\mu$ that are evaluated based
on their corresponding predicate function
$h:\mathbb{R}^{n}\rightarrow\mathbb{R}$ as
$\mu:=\left\\{\begin{array}[]{l}\text{True, \ \ \ \ \ if }h(x)\geq 0\\\
\text{False, \ \ \ \ if }h(x)<0\end{array}\right.$. The syntax for an STL
formula $\phi$ is given by:

$\displaystyle\phi::=\text{True}\mid\mu\mid\neg\phi\mid\phi_{1}\wedge\phi_{2}\mid\phi_{1}U_{[a,b]}\phi_{2}\mid
F_{[a,b]}\phi\mid G_{[a,b]}\phi,$ (25)

where $a,b\in\mathbb{R}^{+}_{0}$ with $a\leq b$, $\phi_{1}$ and $\phi_{2}$ are
STL formulas, $F$ denotes the eventually operator, $G$ denotes the always
operator and $U$ denotes the until operator, each of which is defined below.
The relation $(x,t)\models\phi$ indicates that the signal
$x:\mathbb{R}^{+}_{0}\rightarrow\mathbb{R}^{n}$ satisfies the STL formula
$\phi$ at time $t$.

######  Definition 1.

STL Semantics[5]: The STL semantics for a signal $x$ are recursively defined
as follows:

$\displaystyle(x,t)\models\mu$ $\displaystyle\Leftrightarrow\ h(x)\geq 0$
$\displaystyle(x,t)\models\neg\phi$
$\displaystyle\Leftrightarrow\neg\left(\left(x,t\right)\models\phi\right)$
$\displaystyle(x,t)\models\phi_{1}\wedge\phi_{2}$
$\displaystyle\Leftrightarrow(x,t)\models\phi_{1}\wedge(x,t)\models\phi_{2}$
$\displaystyle(x,t)\models\phi_{1}U_{[a,b]}\phi_{2}$
$\displaystyle\Leftrightarrow\exists
t_{1}\in\left[t+a,t+b\right]s.t.(x,t_{1})\models\phi_{2}$
$\displaystyle\wedge\forall t_{2}\in\left[t,t_{1}\right],(x,t)\models\phi_{1}$
$\displaystyle(x,t)\models F_{[a,b]}\phi$ $\displaystyle\Leftrightarrow\exists
t_{1}\in\left[t+a,t+b\right]s.t.(x,t_{1})\models\phi$
$\displaystyle(x,t)\models G_{[a,b]}\phi$ $\displaystyle\Leftrightarrow\forall
t_{1}\exists\left[t+a,t+b\right],(x,t_{1})\models\phi.$

###  II-D Higher-order Time-varying Control Barrier Functions

Consider a nonlinear control-affine system:

$\displaystyle\dot{x}=f(x)+g(x)u,$ (27)

where $x\in\mathbb{R}^{n}$ is the state of the system and $u\in\mathbb{R}^{m}$
is the control input to the system. Let the relative degree of the system be
$\eta>1$. A time-varying set $\mathcal{C}(t)$ is forward invariant if for a
given control law $u$, there exists a unique solution $x(t)$ to the system
(27) with $x(t_{0})=x_{0}\in\mathcal{C}(t_{0})$ such that $\forall
t\in\left[t_{0},t_{f}\right],x(t)\in\mathcal{C}(t)$. For nonlinear affine
systems (27) with relative degree $\eta>1$, higher order control barrier
functions (HOCBFs)[12][13] can be used to guarantee the forward invariance of
the set $\mathcal{C}(t)$.

######  Definition 2.

HOCBF([13]) A function
$b:\mathbb{R}^{n}\times\mathbb{R}^{+}\rightarrow\mathbb{R}$ is a candidate
higher order control barrier function (HOCBF) of relative degree $\eta$ for
the system defined in (27) if there exists differentiable class $\mathcal{K}$
functions $\alpha_{i},i\in\left\\{1,2,\ldots,\eta\right\\}$ such that

$\displaystyle\begin{split}\sup_{u\in\mathcal{U}}&\left[\mathcal{L}^{\eta}_{f}b(x,t)+\mathcal{L}_{g}\mathcal{L}_{f}^{\eta-1}b(x,t)u+\frac{\partial^{\eta}b(x,t)}{\partial
t^{\eta}}+\alpha_{\eta}(\gamma_{\eta-1}\left(x,t)\right)\right.\\\
&\left.\left(\sum_{i=1}^{\eta-1}\mathcal{L}^{i}_{f}(\alpha_{\eta-i}\circ\gamma_{\eta-i-1})+\frac{\partial^{i}\left(\alpha_{\eta-i}\circ\gamma_{\eta-i-1}\right)}{\partial
t^{i}}\right)\right]\geq 0\end{split}$ (28)

where the functions $\gamma_{i}$ is defined as:

$\displaystyle\gamma_{i}(x,t)=\dot{\gamma}_{i-1}(x,t)+\alpha_{i}\left(\gamma_{i-1}(x,t)\right),\
\ i=\\{1,\ldots,\eta\\}$ (29)

with $\gamma_{0}$ chosen as $\gamma_{0}(x,t)=b(x,t)$.

##  III Temporal Waypoint Navigation of Multi-UAV Payload System

###  III-A HOCBFs for STL Tasks

This subsection discusses how higher-order time-varying control barrier
functions can be used for STL tasks. Consider the following STL fragment:

$\displaystyle\psi::=$ $\displaystyle\ \text{True}\ |\ \mu\ |\ \neg\mu\ |\
\psi_{1}\wedge\psi_{2},$ (30) $\displaystyle\phi::=$ $\displaystyle\
G_{\left[a,b\right]}\psi\ |\ F_{\left[a,b\right]}\psi\ |\
\psi_{1}U_{\left[a,b\right]}\psi_{2}\ |\ \phi_{1}\wedge\phi_{2},$ (31)

where $\psi_{1},\psi_{2}$ are STL formulas for class $\psi$ functions defined
in (30) and $\phi_{1},\phi_{2}$ are STL formulas for class $\phi$ functions
defined in (31). The barrier functions are required to be less than or equal
to their corresponding predicate function between the desired time interval.
For tasks of the form $F_{[a,b]}\mu$ with predicate function $h(x)$, choose
$b(x,t)$ such that $b(x,t^{\prime})\leq h(x)$ for some $t^{\prime}\in[a,b]$.
For tasks of the form $G_{[a,b]}\mu$ with the predicate function $h(x)$,
choose $b(x,t)$ such that $b(x,t^{\prime})\leq h(x)$ for all
$t^{\prime}\in[a,b]$. When there are a conjunction of STL formulas as in (30)
or (31), the following smooth-approximation for minimum operator is used for a
set of $M$ barrier functions with $j=\left\\{1,\ldots,M\right\\}$:

$\displaystyle\min_{j}b_{j}(x,t)\approx-\text{ln}\left(\sum_{j}\text{exp}\left(-b_{j}(x,t)\right)\right).$
(32)

Thus, for tasks of the form $F_{[a,b]}\psi$ where $\psi:=\mu_{1}\wedge\mu_{2}$
with the predicates $h_{1}(x)$ and $h_{2}(x)$ respectively, choose
$b(x,t):=-\text{ln}\left(\text{exp}(-b_{1}(x,t))+\text{exp}(-b_{2}(x,t))\right)$
such that $b_{1}(x,t^{\prime})\leq h_{1}(x)$ and $b_{2}(x,t^{\prime})\leq
h_{2}(x)$ for some $t^{\prime}\in[a,b]$. Similarly, for tasks of the form
$G_{[a,b]}\psi$ where $\psi:=\mu_{1}\wedge\mu_{2}$ with the predicates
$h_{1}(x)$ and $h_{2}(x)$ respectively, choose
$b(x,t):=-\text{ln}\left(\text{exp}(-b_{1}(x,t))+\text{exp}(-b_{2}(x,t))\right)$
such that $b_{1}(x,t^{\prime})\leq h_{1}(x)$ and $b_{2}(x,t^{\prime})\leq
h_{2}(x)$ for all $t^{\prime}\in[a,b]$ and so on. More details on using
barrier functions for STL properties can be found in [6].

Note that the relative degree for the feedback-linearized payload-UAV system
is $\eta=2$. Thus, the control barrier function $b(x,t)$ which is a HOCBF,
must satisfy (28) that can be simplified for $\eta=2$ as follows:

$\displaystyle\begin{split}\underbrace{-\left(\mathcal{L}_{g}\mathcal{L}_{f}b\right)}_{P}u\leq&\
\ \mathcal{L}_{f}^{2}b+\frac{\partial^{2}b}{\partial
t^{2}}+2b\mathcal{L}_{f}b+2b\frac{\partial b}{\partial
t}+\left(\mathcal{L}_{f}b\right)^{2}+\\\ &\underbrace{\left(\frac{\partial
b}{\partial t}\right)^{2}+b^{4}+2\left(\mathcal{L}_{f}b\right)\frac{\partial
b}{\partial t}+2b^{2}\mathcal{L}_{f}b+2b^{2}\frac{\partial b}{\partial
t}}_{H}\end{split}$ (33)

where the class $\mathcal{K}$ functions $\alpha_{i}$’s are chosen as
$\alpha_{i}(s)=s^{2}$ for all $s\in\mathbb{R}_{0}^{+}$ and $\gamma_{0}=b$.
Thus, the STL controller can be formulated as a convex quadratic programming
(CQP) problem as follow:

$\displaystyle\ \ \ \ \ \ \ \ \min_{u}\ \ u^{T}\boldsymbol{Q}u$ (34a)
$\displaystyle\text{s.t.}\ \ \ \ \ \ \ \ \ Pu\leq H$ (34b)

At each time step, the state vector $x$ is obtained and the vectors $P,H$ are
computed using (33), which results in a linear inequality $Pu\leq H$. Thus, at
every time step, the CQP of (34) is solved to obtain the optimal control input
$u$ to the system.

###  III-B Temporal Waypoint Navigation Problem

Consider a series of $M$ waypoints. During the course of waypoint navigation,
it is in general desirable that the payload reaches a particular waypoint
location $\Lambda_{j}\in\mathbb{R}^{3}$ where $j=\left\\{1,\ldots,M\right\\}$
within a certain threshold radius $R_{0}\in\mathbb{R}$, while meeting some
time specifications before moving on to the next waypoint. This requires that
the controller complies with both the spatial as well as the temporal
requirement of the task at hand. For this purpose, a set of time-varying
HOCBFs can be constructed to meet the required specifications. For the
payload-UAV system, the structure of the HOCBFs is chosen as follows:

$\displaystyle
b_{j}\left(x,t\right)=\Gamma_{j}(t)-\left(\left\|r_{0}-\Lambda_{j}\right\|_{2}\right),$
(35)

where $\Gamma_{j}$ is a temporal function. For example, without any loss of
generality, let the payload-UAV system start at the origin. The specifications
to be met are as follows: $\phi:=\phi_{1}\wedge\phi_{2}$, where
$\phi_{1}:=F_{[0,14]}\left(\left\|r_{0}-\left[2\ 2\
2\right]^{T}\right\|_{2}\leq 0.1\right)$ and
$G_{\left[14,25\right]}\left(\left\|r_{0}-\left[2\ 2\
2\right]^{T}\right\|_{2}\leq 3\right)$. This means that the payload must reach
the waypoint location $\Lambda=[2\ 2\ 2]^{T}$ within a radius of $R_{0}=0.1m$
in the time interval $t\in[0,14]$. Once it reaches the specified waypoint, it
must remain at the waypoint location $\Lambda=[2\ 2\ 2]^{T}$ within a radius
of $R_{0}=3m$ in the time interval $t\in[14,25]$. For this specification, the
predicate function $h_{1}$ corresponding to $\phi_{1}$ is given by
$h_{1}(x)=\left(0.1-\left\|r_{0}-\left[2\ 2\ 2\right]^{T}\right\|_{2}\right)$.
Similarly, the predicate function $h_{2}$ corresponding to $\phi_{2}$ is given
by $h_{2}(x)=\left(3-\left\|r_{0}-\left[2\ 2\
2\right]^{T}\right\|_{2}\right)$. The barrier function $b_{1}$ corresponding
to $\phi_{1}$ must satisfy the requirement $b_{1}(x,t)\leq h_{1}(x)$ for some
$t^{\prime}\in[0,14]$. Similarly, the barrier function $b_{2}$ corresponding
to $\phi_{2}$ must satisfy the requirement $b_{2}(x,t)\leq h_{2}(x)$ for all
$t^{\prime}\in[14,25]$. The candidate barrier functions can be chosen as
follows:

$\displaystyle b_{1}(x,t)$
$\displaystyle=\underbrace{\left(50.1-\left(\frac{50}{14}\right)t\right)}_{\Gamma_{1}(t)}-\Big{\|}r_{0}-\underbrace{\left[2\
2\ 2\right]^{T}}_{\Lambda_{1}}\Big{\|}_{2}$ (36a) $\displaystyle b_{2}(x,t)$
$\displaystyle=\underbrace{\left(347.93\cdot
e^{-0.418t}+2\right)}_{\Gamma_{2}(t)}-\Big{\|}r_{0}-\underbrace{\left[2\ 2\
2\right]^{T}}_{\Lambda_{2}}\Big{\|}_{2}$ (36b) $\displaystyle b(x,t)$
$\displaystyle=-\text{ln}\left(e^{-b_{1}(x,t)}+e^{-b_{2}(x,t)}\right)$ (36c)

Note that $b_{1}(x,t)\leq h_{1}(x)$ for some $t^{\prime}\in[0,14]$ and
$b_{2}(x,t)\leq h_{2}(x)$ for all $t^{\prime}\in[14,25]$.

Figure 2: Figure shows the simulation environment in the Gazebo simulator. The
mailboxes represent the location at which the package must be delivered. The
multi-UAV payload system starts at the origin carrying two packages. Once both
the packages are delivered, the payload must reach the hub (shown as a white
cylindrical platform) for refilling purpose.

This can then be extended to a series of $M$ waypoints that require both
spatial as well as temporal specifications. The final barrier function
$b(x,t)$ obtained from (36c) can then be plugged into (33) to generate the
HOCBF constraints. Finally, the CQP problem defined in (34) can be solved to
obtain control inputs in online manner that ensures that the payload-UAV
system meets the temporal waypoint navigation specifications.

##  IV Simulation Results

In order to validate the proposed STL controller in (34), a high-fidelity
Gazebo simulation is conducted. The rotorS MAV simulator package [14] is used
to spawn four UAVs that are connected to a rectangular payload via four rigid
links. The software stack consists of custom Gazebo plugins that simulate GPS
and IMU sensors. The entire payload-UAV model is spawned using .xacro files
and the proposed control algorithm is implemented inside a ROS C++ script. The
control algorithm runs at a sampling rate of $50Hz$. The simulation is
conducted on a 3.2GHz Intel i7 processor with 8GB RAM and NVIDIA 1050Ti
graphics driver.

Figure 3: Figure shows 4 Hummingbird UAVs connected to the vertical links
through spherical joints. There are two packages on the payload, which the
UAVs must transport to the required destination under certain time
specifications.

The multi-UAV payload system is shown in Fig. 3. It consists of four
Hummingbird UAVs that are connected to the four vertical rods via spherical
joints (modelled as two revolute joints in .xacro file). The vertical rods are
rigidly connected to the payload and thus, cannot move. The payload carries
two packages that are to be delivered at specific locations with certain time
specifications.

Table I: Parameters for the multi-UAV payload system | $m$ | $J_{xx}$ | $J_{yy}$ | $J_{zz}$
---|---|---|---|---
Payload | 1.0 | 0.556 | 0.556 | 0.556
UAVs | 0.68 | 0.029 | 0.029 | 0.055
|  | $\rho_{i}$ |  | $l_{i}$
UAV1 |  | $[0.25\ \ \ \ \ 0.25\ \ \ \ \ 0.125]^{T}$ |  | 3.2
UAV2 |  | $[0.25\ \ \ \ \shortminus 0.25\ \ \ \ 0.125]^{T}$ |  | 3.2
UAV3 |  | $[\shortminus 0.25\ \ \ \shortminus 0.25\ \ \ 0.125]^{T}$ |  | 3.2
UAV4 |  | $[\shortminus 0.25\ \ \ \ \ 0.25\ \ \ \ \ 0.125]^{T}$ |  | 3.2

Figure 4: Figure shows the variation of $x$, $y$, and $z$ position of the
payload with respect to time. The grey regions indicate the envelope of the
corresponding temporal function.

Consider a typical package delivery scenario where the UAVs must
collaboratively transport the payload carrying multiple packages from one
point to another. For the sake of simulation purposes, consider that there are
two packages on the payload that must be delivered at different locations with
some temporal specifications. The payload must arrive at
$\Lambda_{1}=(10,10,5)$ to deliver the first package between the time interval
$[0,18]$ and stay there till $t=30s$ within a tolerance radius of $R_{0}=1.0$.
The payload must then arrive at $\Lambda_{2}=(25,10,5)$ to deliver the second
package between the time interval $[30,48]$ and stay there till $t=60s$ within
the tolerance radius of $R_{0}=1.0$. Finally, the empty payload must land at
the hub located at $\Lambda_{3}=(40,20,1)$ for refilling within the time
interval $[60,78]$ and stay there till $t=90s$ within the tolerance radius of
$R_{0}=1.0$. These requirements can be captured in the following STL
specification $\phi:=\phi_{1}\wedge\phi_{2}\wedge\phi_{3}\wedge\phi_{4}$
where,

$\displaystyle\begin{split}\phi_{1}:=&F_{[0,18]}\left(\left\|r_{0}-\left[10\
10\ 5\right]^{T}\right\|_{2}\leq 1.0\right)\wedge\ \\\
&G_{[17,30]}\left(\left\|r_{0}-\left[10\ 10\ 5\right]^{T}\right\|_{2}\leq
1.0\right)\end{split}$ (37)
$\displaystyle\begin{split}\phi_{2}:=&F_{[30,48]}\left(\left\|r_{0}-\left[25\
10\ 5\right]^{T}\right\|_{2}\leq 1.0\right)\wedge\\\
&G_{[47,60]}\left(\left\|r_{0}-\left[25\ 10\ 5\right]^{T}\right\|_{2}\leq
1.0\right)\end{split}$ (38)
$\displaystyle\begin{split}\phi_{3}:=&F_{[60,78]}\left(\left\|r_{0}-\left[40\
20\ 1\right]^{T}\right\|_{2}\leq 1.0\right)\wedge\\\
&G_{[77,90]}\left(\left\|r_{0}-\left[40\ 20\ 1\right]^{T}\right\|_{2}\leq
1.0\right)\end{split}$ (39)

$\displaystyle\phi_{4}:=G_{[0,90]}\left(\left\|r_{0}\right\|_{\infty}\leq
50\right)\ \ \ $ (40)

The specification $\phi_{4}$ in (40) ensures that the payload always remains
inside a safe cuboid of side $50m$ centered at the origin.

Figure 5: Figure shows the variation of the time-varying barrier function
$b(x,t)$ with respect to time.

The entire simulation environment is shown in Fig. 2. It consists of two
mailboxes positioned at $\Lambda_{1}$ and $\Lambda_{2}$ respectively. While
delivering the packages, the payload’s center of mass must be within the green
translucent cylinders that have a radius equal to $R_{0}$ which is the
tolerance radius in the horizontal plane. Once delivered, the UAVs must land
the payload on the white circular hub located at $\Lambda_{3}$. The simulation
video is available here111The video demonstration is available on this link if
the pop-up doesn’t work: https://youtu.be/T1MYlKHaMkw.

The payload trajectory in individual axis is shown in Fig. 4 along with the
time envelopes of the respective temporal functions $\Gamma_{j}(t)$. It can be
seen that the controller satisfies all the temporal specifications while
navigating through each of the waypoints. The values for time-varying barrier
function $b(x,t)$ are provided in Fig. 5.

##  V Conclusions

In this paper, the problem of temporal waypoint navigation for multi-UAV
payload systems is addressed. The $N$ UAVs are attached to rigid rods via
spherical joints. These rods are connected to the payload rigidly and thus
remain vertical always. This system’s complex nonlinear state-space equations
are simplified by applying input-output feedback linearization to the
payload’s translational dynamics. The Signal Temporal Logic Specifications are
captured using higher-order time-varying control barrier functions to
formulate an optimization-based control law. The controller’s efficacy and
real-time implementability are demonstrated by simulating a package delivery
scenario in a high-fidelity Gazebo simulator.

## References

  * [1] T. Lee, “Geometric control of quadrotor UAVs transporting a cable-suspended rigid body,” _IEEE Transactions on Control Systems Technology_ , vol. 26, no. 1, pp. 255–264, 2017.
  * [2] J. Wehbeh, S. Rahman, and I. Sharf, “Distributed model predictive control for UAVs collaborative payload transport,” in _2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)_. IEEE, 2020, pp. 11 666–11 672.
  * [3] X. Jin and Z. Hu, “Adaptive cooperative load transportation by a team of quadrotors with multiple constraint requirements,” _IEEE Transactions on Intelligent Transportation Systems_ , pp. 1–14, 2022.
  * [4] N. Rao and S. Sundaram, “An input-output feedback linearization based exponentially stable controller for multi-UAV payload transport,” _arXiv preprint arXiv:2207.04375_ , 2022.
  * [5] O. Maler and D. Nickovic, “Monitoring temporal properties of continuous signals,” in _Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems_. Springer, 2004, pp. 152–166.
  * [6] L. Lindemann and D. V. Dimarogonas, “Control barrier functions for signal temporal logic tasks,” _IEEE control systems letters_ , vol. 3, no. 1, pp. 96–101, 2018.
  * [7] A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” _IEEE Transactions on Automatic Control_ , vol. 62, no. 8, pp. 3861–3876, 2016.
  * [8] A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, “Control barrier functions: Theory and applications,” in _2019 18th European control conference (ECC)_. IEEE, 2019, pp. 3420–3431.
  * [9] Y. V. Pant, H. Yin, M. Arcak, and S. A. Seshia, “Co-design of control and planning for multi-rotor UAVs with signal temporal logic specifications,” in _2021 American Control Conference (ACC)_. IEEE, 2021, pp. 4209–4216.
  * [10] Y. V. Pant, H. Abbas, R. A. Quaye, and R. Mangharam, “Fly-by-logic: Control of multi-drone fleets with temporal logic objectives,” in _2018 ACM/IEEE 9th International Conference on Cyber-Physical Systems (ICCPS)_. IEEE, 2018, pp. 186–197.
  * [11] L. Lindemann and D. V. Dimarogonas, “Barrier function based collaborative control of multiple robots under signal temporal logic tasks,” _IEEE Transactions on Control of Network Systems_ , vol. 7, no. 4, pp. 1916–1928, 2020\.
  * [12] X. Xu, “Constrained control of input–output linearizable systems using control sharing barrier functions,” _Automatica_ , vol. 87, pp. 195–201, 2018.
  * [13] W. Xiao and C. Belta, “High order control barrier functions,” _IEEE Transactions on Automatic Control_ , 2021.
  * [14] F. Furrer, M. Burri, M. Achtelik, and R. Siegwart, _Robot Operating System (ROS): The Complete Reference (Volume 1)_. Cham: Springer International Publishing, 2016, ch. RotorS—A Modular Gazebo MAV Simulator Framework, pp. 595–625. [Online]. Available: http://dx.doi.org/10.1007/978-3-319-26054-9_23


# Frustratingly Simple Prompting-based Text Denoising

Jungyeul Park
Department of Linguistics
The University of British Columbia
Vancouver, BC V6T 1Z4, Canada
<EMAIL_ADDRESS>
Mengyang Qiu
Department of Psychology
Trent University
Peterborough, ON K9L 0G2, Canada
<EMAIL_ADDRESS>This work was supported in part by Oracle Cloud credits
and related resources provided by Oracle for Research.

###### Abstract

This paper introduces a novel perspective on the automated essay scoring (AES)
task, challenging the conventional view of the ASAP dataset as a static
entity. Employing simple text denoising techniques using prompting, we explore
the dynamic potential within the dataset. While acknowledging the previous
emphasis on building regression systems, our paper underscores how making
minor changes to a dataset through text denoising can enhance the final
results.

##  1 Introduction

Text denoising is a crucial step in natural language processing (NLP) and text
analysis tasks (Sun & Jiang, 2019; Xian et al., 2021). One of its major
applications is in optical character recognition (OCR). Recently, the
technique has also found utility in image caption editing, where computer
vision and natural language processing intersect (Wang et al., 2022; Yuan et
al., 2023). Despite its significance, in written text processing, the task of
text denoising has often been overlooked due to the perception that the
provided datasets are already well-prepared. Prompting has proven successful
in the text transfer task, even with small language models (Suzgun et al.,
2022). Therefore, we approach the processing of written text as a form of text
transfer, employing prompting.

In the text denoising experiment, our objective is to clean the dataset used
for automated essay scoring (AES) in preparation for the linear regression
task. AES involves the use of an automated system to assign numerical grades
or scores to essays written in a first language (L1) within an educational
setting. It is crucial to note that English AES systems rely on the ASAP
dataset, initially provided in the Kaggle competition of
2012.111https://www.kaggle.com/c/asap-aes This dataset has become widely
adopted in various AES systems (Alikaniotis et al., 2016; Cummins et al.,
2016; Dong et al., 2017; Ridley et al., 2021; Chen & Li, 2023; Do et al.,
2023). The original ASAP dataset employed a named entity recognition approach
using Stanford CoreNLP (Manning et al., 2014) and a range of pattern matching
rules to eliminate personally identifying information from the essays.
Consequently, entities within the text are identified and replaced with
strings initiated with the ‘@’ symbol, such as @PERSON1. Furthermore, more
than 5% of sentences exhibit encoding issues where UTF-8 symbols are not
correctly displayed, in addition to the presence of non-word entities.

We classify sentences containing encoding issues and non-word entities as
noise, and subsequently, undergo a denoising process to address them. Our
hypothesis posits that enhancing text quality through denoising will yield
improved linear regression results in AES. Throughout this paper, we use the
term prompt in two distinct contexts: (1) In the context of essay writing, a
prompt refers to a specific question, topic, or statement serving as the
starting point for the essay. (2) In the context of generative pre-trained
transformers, a prompt denotes the input or stimulus provided to the model to
generate a response.

##  2 Text denoising

In the context of the ASAP dataset, Figure 1 illustrates an instance of text
denoising. For this process, we employ two prompts with gpt-3.5-turbo-
instruct: one to address encoding errors and another to replace non-word
entities with arbitrary entity names sequentially.222The prompting process
costs $6.87 for the entire 12,978 ASAP data entries, where we select sentences
containing only such encoding errors and non-word entities. It is noteworthy
that gpt-3.5-turbo-instruct has a tendency to correct grammatical errors in
the original text during sentence generation. To restore the original words,
we utilize the .m2 annotation generated by ERRANT (Bryant et al., 2017). This
annotation delineates the modifications made in the original text, allowing us
to retain only the symbols with corrected encoding and the replaced non-word
entities.

Original text: |  people get @CAPS2 addicted that they don<U+0092>t exercize and become obeast, ...
---|---
Cleaned text: |  people get too addicted that they don’t exercize and become obeast, ...

Figure 1: Example of text denoising: the Unicode symbol U+0092 is replaced
with ’, and @CAPS2 is substituted with an arbitrary word

##  3 Experiments and Results

After text denoising, we utilize roberta-base (Liu et al., 2019) for the
linear regression task to derive the overall score. The results of the linear
regression by quadratic weighted kappa (QWK), along with perplexity values,
are presented in Table 1 for both the original and cleaned texts. It’s
important to note that all linear regression evaluations are conducted on the
original text, even when the model is trained using the cleaned text, ensuring
a fair comparison. We employ prompt-based 8-fold cross-validation, considering
ASAP’s eight different prompt essay sets, and the results represent the
average overall scores.

| Sentence ppl | Token ppl | Regression
---|---|---|---
Original text | 532.571 | 65.535 | 0.6047
Cleaned text | 520.023 | 51.097 | 0.6143
Table 1: Experiment results, including perplexity and regression using QWK

##  4 Discussion and Conclusion

The ASAP dataset is often regarded as a given, with prior research primarily
concentrating on constructing a regression system. However, making even subtle
modifications through denoising to the dataset can yield improved results. In
the previous automatic writing evaluation system for L2 writing, Lim et al.
(2023) observed that attention did not focus on spelling errors. Rather, a
pre-trained large language model can be associated with more proper words
instead of spelling errors to predict results. Through the cleaning process of
the training dataset, we confirm their finding that the refined training
dataset exhibits enhanced learning capabilities, leading to more accurate
result prediction.

A closer examination of the prompt-by-prompt QWK results reveals insightful
nuances. In most cases, the cleaned text surpasses the original text,
underscoring the efficacy of the denoising process. While the effectiveness of
text denoising is evident, the nuanced variations across prompts necessitate
careful consideration in experimental design. As we explore these avenues, we
anticipate that refining the dataset and incorporating additional features
will contribute to the ongoing improvement of automated essay scoring systems.
The limitation of our study still lies in the choice of employing a simple
transformer for the regression task instead of building our own neural
regression system. As a result, despite our inability to achieve state-of-the-
art results for the ASAP dataset, as demonstrated by previous neural AES
systems incorporating numerous linguistic features (Ridley et al., 2021; Chen
& Li, 2023; Do et al., 2023), our approach yields relatively good results with
minimal effort.

#### URM Statement

The authors acknowledge that both authors of this work meet the URM criteria
of ICLR 2024 Tiny Papers Track.

## References

  * Alikaniotis et al. (2016) Dimitrios Alikaniotis, Helen Yannakoudakis, and Marek Rei.  Automatic Text Scoring Using Neural Networks.  In _Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pp. 715–725, Berlin, Germany, 8 2016. Association for Computational Linguistics.  doi: 10.18653/v1/P16-1068.  URL https://aclanthology.org/P16-1068.
  * Bryant et al. (2017) Christopher Bryant, Mariano Felice, and Ted Briscoe.  Automatic Annotation and Evaluation of Error Types for Grammatical Error Correction.  In _Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pp. 793–805, Vancouver, Canada, 2017. Association for Computational Linguistics.  URL http://aclweb.org/anthology/P17-1074.
  * Chen & Li (2023) Yuan Chen and Xia Li.  PMAES: Prompt-mapping Contrastive Learning for Cross-prompt Automated Essay Scoring.  In _Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pp. 1489–1503, Toronto, Canada, 7 2023. Association for Computational Linguistics.  URL https://aclanthology.org/2023.acl-long.83.
  * Cummins et al. (2016) Ronan Cummins, Meng Zhang, and Ted Briscoe.  Constrained Multi-Task Learning for Automated Essay Scoring.  In _Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)_ , pp. 789–799, Berlin, Germany, 8 2016. Association for Computational Linguistics.  doi: 10.18653/v1/P16-1075.  URL https://aclanthology.org/P16-1075.
  * Do et al. (2023) Heejin Do, Yunsu Kim, and Gary Geunbae Lee.  Prompt- and Trait Relation-aware Cross-prompt Essay Trait Scoring.  In _Findings of the Association for Computational Linguistics: ACL 2023_ , pp. 1538–1551, Toronto, Canada, 7 2023. Association for Computational Linguistics.  URL https://aclanthology.org/2023.findings-acl.98.
  * Dong et al. (2017) Fei Dong, Yue Zhang, and Jie Yang.  Attention-based Recurrent Convolutional Neural Network for Automatic Essay Scoring.  In _Proceedings of the 21st Conference on Computational Natural Language Learning (CoNLL 2017)_ , pp. 153–162, Vancouver, Canada, 8 2017. Association for Computational Linguistics.  doi: 10.18653/v1/K17-1017.  URL https://aclanthology.org/K17-1017.
  * Lim et al. (2023) KyungTae Lim, Jayoung Song, and Jungyeul Park.  Neural automated writing evaluation for Korean L2 writing.  _Natural Language Engineering_ , 29(5):1341–1363, 2023.  doi: 10.1017/S1351324922000298.  URL https://www.cambridge.org/core/journals/natural-language-engineering/article/neural-automated-writing-evaluation-for-korean-l2-writing/C1C7090E7DB7F0756CCD0B4B002E096A.
  * Liu et al. (2019) Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov.  RoBERTa: A Robustly Optimized BERT Pretraining Approach.  _CoRR_ , abs/1907.1, 2019.  URL http://arxiv.org/abs/1907.11692.
  * Manning et al. (2014) Christopher D. Manning, Mihai Surdeanu, John Bauer, Jenny Rose Finkel, Steven Bethard, and David McClosky.  The Stanford CoreNLP Natural Language Processing Toolkit.  In _Proceedings of 52nd Annual Meeting of the Association for Computational Linguistics: System Demonstrations_ , pp. 55–60, Baltimore, Maryland, 6 2014. Association for Computational Linguistics.  URL http://www.aclweb.org/anthology/P14-5010.
  * Ridley et al. (2021) Robert Ridley, Liang He, Xin-yu Dai, Shujian Huang, and Jiajun Chen.  Automated Cross-prompt Scoring of Essay Traits.  _Proceedings of the AAAI Conference on Artificial Intelligence_ , 35(15):13745–13753, 5 2021.  URL https://ojs.aaai.org/index.php/AAAI/article/view/17620.
  * Sun & Jiang (2019) Yifu Sun and Haoming Jiang.  Contextual Text Denoising with Masked Language Model.  In _Proceedings of the 5th Workshop on Noisy User-generated Text (W-NUT 2019)_ , pp. 286–290, Hong Kong, China, 11 2019. Association for Computational Linguistics.  doi: 10.18653/v1/D19-5537.  URL https://aclanthology.org/D19-5537.
  * Suzgun et al. (2022) Mirac Suzgun, Luke Melas-Kyriazi, and Dan Jurafsky.  Prompt-and-Rerank: A Method for Zero-Shot and Few-Shot Arbitrary Textual Style Transfer with Small Language Models.  In _Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing_ , pp. 2195–2222, Abu Dhabi, United Arab Emirates, 12 2022. Association for Computational Linguistics.  URL https://aclanthology.org/2022.emnlp-main.141.
  * Wang et al. (2022) Zhen Wang, Long Chen, Wenbo Ma, Guangxing Han, Yulei Niu, Jian Shao, and Jun Xiao.  Explicit Image Caption Editing.  In Shai Avidan, Gabriel Brostow, Moustapha Cissé, Giovanni Maria Farinella, and Tal Hassner (eds.), _Computer Vision – ECCV 2022_ , pp. 113–129, Cham, 2022. Springer Nature Switzerland.  ISBN 978-3-031-20059-5.
  * Xian et al. (2021) Jiayi Xian, Dingcheng Li, Alexander Hanbo Li, Derek Liu, Xing Fan, Edward Guo, Yang Liu, and Yuqing Tang.  Unified denoising pretraining and finetuning for data and text.  In _WeCNLP 2021_ , Virtually, 2021. wecnlp.ai.  URL https://www.amazon.science/publications/unified-denoising-pretraining-and-finetuning-for-data-and-text.
  * Yuan et al. (2023) Mengqi Yuan, Bing-Kun Bao, Zhiyi Tan, and Changsheng Xu.  Adaptive Text Denoising Network for Image Caption Editing.  _ACM Transactions on Multimedia Computing, Communications, and Applications_ , 19(1s), 2 2023.  ISSN 1551-6857.  doi: 10.1145/3532627.  URL https://doi.org/10.1145/3532627.

##  Appendix A Appendix

###  A.1 Restoring the original text from gpt-corrected text

We use the following two prompts with gpt-3.5-turbo-instruct for text
denoising:

  1. 1.

Copy the sentence by replacing utf8 encoding error characters into the correct
ascii symbols

  2. 2.

Copy the sentence by replacing @words into the real words

After obtaining the text generated by gpt, the errant_parallel tool produces
the .m2 file. The annotations in the .m2 file reveal the results of the
prompting process, which involves fixing encoding errors and replacing non-
word entities.

    S 682|1|2 I think this because mere cases of suicide are from online bullying,
    people get @CAPS2 addicted that they don<U+0092>t exercize and become obeast,
    and because it is bad for the environment.
    A 0 1|||U:OTHER||||||REQUIRED|||-NONE-|||0
    A 19 20|||R:VERB|||don’t|||REQUIRED|||-NONE-|||0        (***)
    A 20 21|||R:SPELL|||exercise|||REQUIRED|||-NONE-|||0
    A 23 24|||R:OTHER|||obese,|||REQUIRED|||-NONE-|||0

    S 682|1|2 I think this because mere cases of suicide are from online bullying,
    people get @CAPS2 addicted that they don’t exercize and become obeast, and
    because it is bad for the environment.
    A 0 1|||U:OTHER||||||REQUIRED|||-NONE-|||0
    A 5 6|||R:ADJ|||many|||REQUIRED|||-NONE-|||0
    A 10 11|||R:OTHER|||caused by|||REQUIRED|||-NONE-|||0
    A 13 14|||R:NOUN|||individuals|||REQUIRED|||-NONE-|||0
    A 15 16|||R:OTHER|||too|||REQUIRED|||-NONE-|||0         (***)
    A 20 21|||R:SPELL|||exercise|||REQUIRED|||-NONE-|||0
    A 23 24|||R:OTHER|||obese,|||REQUIRED|||-NONE-|||0
    A 28 29|||R:ADJ|||harmful|||REQUIRED|||-NONE-|||0
    A 29 30|||R:PREP|||to|||REQUIRED|||-NONE-|||0

where S 682|1|2 represents source, the ASAP id, the prompt number, and the
sentence id, respectively. We retain only the encoding errors and replace non-
word entities in As (the annotations corrected by gpt) marked with (***).
ERRANT enables us to regenerate the corrected sentence using the corresponding
annotation information: people get too addicted that they don’t exercize and
become obeast, … as in the original text, instead of people get too addicted
that they don’t exercise and become obese, … as gpt generated.

###  A.2 Detailed experiment results

Detailed prompt-by-prompt results are presented in Table 2, including the
outcomes of encoding fixed without replacing non-word entities (Encoding
fixed), the evaluation conducted on the corresponding dataset rather than
using the original text (Cleaned’), and the evaluation conducted on the
original text to ensure a fair comparison (Cleaned) as in Table 1. During
training, we utilize the default values of the Trainer
class,333https://huggingface.co/docs/transformers/main_classes/trainer
employing the RoBERTa base model. We normalize the score to the range of 0 and
1, and we multiply the results by 100 to calculate QWK using the standard
evaluation script provided by ets.org.

| Prompt 1 | Prompt 2 | Prompt 3 | Prompt 4 | Prompt 5 | Prompt 6 | Prompt 7 | Prompt 8 | Average
---|---|---|---|---|---|---|---|---|---
Original | 0.6187 | 0.6308 | 0.6962 | 0.6626 | 0.7158 | 0.5924 | 0.4622 | 0.4586 | 0.6047
Encoding fixed | 0.6517 | 0.5855 | 0.6872 | 0.6290 | 0.7485 | 0.6174 | 0.4692 | 0.4943 | 0.6103
Cleaned’ | 0.7193 | 0.5414 | 0.6906 | 0.6454 | 0.7374 | 0.6187 | 0.4441 | 0.4442 | 0.6052
Cleaned | 0.7344 | 0.5485 | 0.6978 | 0.6540 | 0.7416 | 0.6156 | 0.4637 | 0.4589 | 0.6143

Table 2: Prompt-by-prompt QWK results: e.g. prompt 1 represents that prompt 1
is used as a test set, and prompts 2-7 as a training set, and prompt 8 as a
dev set.

We present a comprehensive set of results utilizing various metrics in Table
3, including: Quadratic Weighted Kappa (QWK), Kendall Rank Coefficient (KRC),
Spearman Rank Correlation (SRC), Pearson Correlation Coefficient (PCC), Mean
Squared Error (MSE), and Root-Mean-Square Deviation or Root-Mean-Square Error
(RMSD). This diverse range of metrics provides a thorough evaluation of our
results from different perspectives.

| QWK | KRC | SRC | PCC | MSE | RMSD
---|---|---|---|---|---|---
Original | 0.6047 | 0.5477 | 0.6867 | 0.7062 | 0.0295 | 0.1676
Encoding fixed | 0.6103 | 0.5426 | 0.6810 | 0.6982 | 0.0288 | 0.1652
Cleaned all’ | 0.6052 | 0.5479 | 0.6869 | 0.7050 | 0.0296 | 0.1675
Cleaned all | 0.6143 | 0.5432 | 0.6813 | 0.7016 | 0.0287 | 0.1645
Table 3: Detailed results using various metrics.