# Shape matters: long-range transport of microplastic fibers in the atmosphere

Daria Tatsii  Department of Meteorology and Geophysics, University of Vienna,
Universitätsring 1, 1010, Vienna, Austria<EMAIL_ADDRESS>Silvia
Bucci  Department of Meteorology and Geophysics, University of Vienna,
Universitätsring 1, 1010, Vienna, Austria  Taraprasad Bhowmick  Laboratory for
Fluid Physics, Pattern Formation and Biocomplexity, Max Planck Institute for
Dynamics and Self-Organisation, Am Faßberg 17, 37077, Göttingen, Germany
Johannes Guettler  Laboratory for Fluid Physics, Pattern Formation and
Biocomplexity, Max Planck Institute for Dynamics and Self-Organisation, Am
Faßberg 17, 37077, Göttingen, Germany  Lucie Bakels  Department of Meteorology
and Geophysics, University of Vienna, Universitätsring 1, 1010, Vienna,
Austria  Gholamhossein Bagheri  Laboratory for Fluid Physics, Pattern
Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-
Organisation, Am Faßberg 17, 37077, Göttingen, Germany
<EMAIL_ADDRESS>Andreas Stohl  Department of Meteorology and
Geophysics, University of Vienna, Universitätsring 1, 1010, Vienna, Austria

###### Abstract

Deposition of giant microplastic particles from the atmosphere has been
observed in the most remote places on Earth. However, their deposition
patterns are difficult to reproduce using current atmospheric transport
models. These models usually treat particles as perfect spheres, whereas the
real shapes of microplastic particles are often far from spherical. Such
particles experience lower settling velocities compared to volume-equivalent
spheres, leading to longer atmospheric transport. Here, we present novel
laboratory experiments on the gravitational settling of microplastic fibers in
air and find that their settling velocities are reduced by up to 76$\%$
compared to spheres of the same volume. An atmospheric transport model
constrained with the experimental data shows that shape-corrected settling
velocities significantly increase the horizontal and vertical transport of
particles. Our model results show that microplastic fibers of about
$1\text{\,}\mathrm{mm}$ length emitted in populated areas can reach extremely
remote regions of the globe, including the High Arctic, which is not the case
for spheres. We also calculate that fibers with lengths of up to
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ settle slowly enough to be lifted
high into the stratosphere, where degradation by ultraviolet radiation may
release chlorine and bromine, thus potentially damaging the stratospheric
ozone layer. These findings suggest that the growing environmental burden and
still increasing emissions of plastics pose multiple threats to life on Earth.

###### keywords:

microplastics $|$ shape $|$ atmospheric transport $|$ gravitational settling

Institute for the Dynamics of Complex Systems, University of Göttingen,
Friedrich-Hund-Platz 1, 37077, Göttingen, Germany Contributed equally to this
work Contributed equally to this work

##  1 Introduction

Airborne particles have a large impact on Earth’s energy balance, atmospheric
composition, water and carbon cycles, ecosystems, and human health 1.
Therefore, it is crucial to know their distribution in the global atmosphere,
for which an accurate understanding of their emissions and removal mechanisms
is essential. Accumulation mode particles sized 100-1000 nm are known to be
transported over long distances in the atmosphere2, sometimes across an entire
hemisphere 3. However, several studies 4, 5, 6, 7, 8, 9 have found that even
”giant” particles larger than $75\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in
diameter can stay airborne for extended periods and be deposited thousands of
kilometers away from their sources. This is difficult to reproduce with
current atmospheric transport models, which predict a much shorter dispersion
range for such large particles 10, 11. The question is what mechanisms or
model deficiencies can explain these discrepancies.

Several mechanisms that have been suggested to enhance transport distances,
for instance, strong winds 12, strong turbulence keeping individual particles
aloft 13, or electric forces counteracting the particles’ weight 14, 15 seem
insufficient to resolve the model problems. Another possibility investigated
in this paper is the effect of particle shape. Most regional or global
transport models treat particles as perfect spheres, whereas in reality, their
shapes are often far from spherical. Such particles experience a larger drag
in the atmosphere compared to spheres, which reduces their settling velocity
and facilitates longer transport distances 16. This is particularly true for
microplastics, which are often found as fibers or with other complex shapes in
the environment and also have a lower density than many other aerosol types
17, 18, 19, 20, 21, 22, 23.

To date, shape corrections for gravitational settling calculations24 have been
mostly used for modeling dispersion of volcanic ash 16 and mineral dust 25.
However, microplastic fibers with lengths that exceed their thickness by a
factor of 40 or more, represent a greater challenge. While their settling
behavior in water or other liquids is already relatively well-constrained,
only a few experiments have investigated the settling of non-spherical
particles in air 26, 24, 27, 28 and the available data do not cover the range
of sizes and shapes relevant to microplastics. In particular, data on the
settling behavior of fibers, especially of bent shapes, are missing and this
limits our capability to reliably simulate the dispersion of microplastics in
the atmosphere.

To determine the settling velocities of microplastic fibers of different sizes
and shapes, we performed a series of experiments in a newly developed setup
(SI Figure S1a) 26. Particles with a mass density of
$1200\text{\,}\mathrm{kg}\text{\,}{\mathrm{m}}^{-3}$, typical of common
plastic polymers, and of various shapes including spheres, straight fibers,
and curved fibers with semi- and quarter-circular shapes with aspect ratios AR
(the ratio of the fiber length to its diameter) of 20, 50, and 100 were
produced using 3D printing technology 29 (Figure 1a). Detailed information
about the experiments can be found in Methods.

Figure 1: Example of the particles printed for the experiments and settling
behavior of fibers.(a) Straight, semicircular, and quarter circular
$1\text{\,}\mathrm{mm}$ fibers for different aspect ratios AR, and the
corresponding diameters $d_{eq}$ of volume equivalent spheres (sizes of other
printed particles are listed in SI Table S1). Snapshots of the
$1\text{\,}\mathrm{mm}$ (b-d) fibers with aspect ratio AR $=20$, indicating
their settling behavior under gravity. The snapshots correspond to the last
$6.6\text{\,}\mathrm{mm}$ of recording by the bottom cameras BX and BY from
the experiments with (b) straight, (c) semicircular, and (d) quarter circular
fibers. BX and BY refer to lower cameras with field of view perpendicular to
each other. $g$ shows the gravity vector. $d_{eq}$, i.e. the equivalent-volume
diameter, is the diameter of a sphere with the same volume as the particle.

## Results and Discussion

Our experimental results reveal that the measured terminal settling velocities
for straight fibers, semicircular and quarter circular fibers are only
24-51$\%$ of the velocities of spheres with the same volume (Figure 2a, SI
Table S1). The largest differences are found for the particles with the
largest aspect ratios (AR $=100$), for which the settling velocities are less
than one-third of those for spheres of the same volume. For a given volume and
aspect ratio, the differences between the velocities of straight,
semicircular, and quarter circular fibers are relatively small (on average,
12$\%$ with a maximum deviation of $\sim$26$\%$ for particles of size of 1000
µm x 10 µm). Nevertheless, straight fibers have the lowest and semicircular
fibers the highest settling velocities. On average, straight fibers settle
with 38$\%$ (minimum value of 24$\%$) and semicircular fibers with 41$\%$
(minimum value of 29$\%$) of the velocity of spheres of the same volume. In
addition to the settling velocities of the fibers, we also studied their
orientation dynamics and the interplay of these dynamics in the turbulent
atmosphere. Figure S1c-h (Supporting Information) show exemplary super-imposed
images from particles falling through the lower region of the field of view of
the bottom cameras, where the fibers had already reached a steady-state
velocity.

Figure 2: Observed and modeled gravitational settling velocities.(a) Settling
velocities as a function of particle size, expressed as the diameter of a
sphere of equivalent volume. Modeled values using the shape correction scheme
for averaged orientation are shown as a black dashed line for spheres and as
colored shaded areas covering the range of aspect ratios from 20 to 100 for
straight (blue), semicircular (purple) and quarter circular (red) fibers.
Experimental mean values for each shape are represented by open markers, coded
by color for shape type and by thickness for aspect ratio. The spread in the
results of repeated experiments for individual particle types is smaller than
the size of the symbols. The inset gives an example of the experimental data
spread for a limited size range on a linear velocity scale (semitransparent
blue dots for straight fibers, purple dots for semicircular fibers, red dots
for quarter circular fibers). Black dots show the calculated settling
velocities of spheres with volumes equivalent to the experimentally studied
fibers. (b) Scatter plot of observed and modeled settling velocities. Modeled
values were calculated for random (purple), maximum-drag (pink) and averaged
(red) orientations. Black open rhombuses show previously published
experimental results by Qi et. al30 and Jayaweera and Cottis (1969) 28.
Particle shapes are distinguished as reported in the legend in panel a. The
inset zooms on the smallest settling velocities.

We find in similitude with previous work 26, 30, 27 that fiber-like particles
achieve a terminal stable orientation with their maximum projection area
perpendicular to the settling direction. Beyond the existing knowledge, we
further observe that depending on their aspect ratio, fibers can approach
their steady-state orientation with or without oscillations, which is in
agreement with the theoretical predictions about oscillations in Figure 4 of
Bhowmick et al 26. In particular, the fiber oscillations decrease as the fiber
diameter decreases (SI Figure S4). For example, regardless of their shape, the
fibers with $1\text{\,}\mathrm{mm}$ length and AR $=20$ had reached both their
steady-state orientation and settling velocity in the section observed by the
bottom cameras (SI Figure S1c-e). Their oscillations in orientation were
already dampened when they fell through the section observed by the top
cameras (SI Figure S4a-c). In contrast, the fibers with
$2\text{\,}\mathrm{mm}$ length and AR $=20$ did not reach a steady-state
orientation for the entire duration of the camera recording but they had
nevertheless reached a steady-state settling velocity when observed by the
bottom cameras (SI Figure S1f-h, Figure S4e-g, and S10). This is because the
settling velocity responds to orientation changes only on time scales longer
than the period of orientation oscillations. In fact, our experiments reveal
that the fiber oscillations decay exponentially in air, with a decay constant
of the order of $10\text{\,}\mathrm{ms}$. Therefore, the time scales for
alignment in fiber orientation are smaller than the smallest time scales
typically encountered in atmospheric turbulence. An important implication of
these new findings is that the orientation of the investigated fibers with
respect to the gravity vector is similar in the turbulent atmosphere and in
still air. In situations when these fibers encounter highly turbulent regions
of the atmosphere such as in clouds, fiber orientation may become random.
However, the deviations from the measurements made here would be negligible
because (i) these events would be brief compared to the residence time of the
fibers in the atmosphere, and (ii) even model calculations for randomly
oriented fibers deviate only by about 17$\%$ from our measurements (SI Table
S2).

Recently, the model of Bagheri and Bonadonna (2016) 24 was shown to be
associated with small errors in estimating the settling velocity of
microplastics of various shapes in water 31. The model can be fitted to
predict the settling velocity for non-spherical particles when they fall with
their minimum, maximum, or random projection areas facing downward, and it is
also applicable to settling in air (see Methods). Figure 2b compares this
model with the observations. With its maximum drag orientation configuration,
the model agrees well with the measurements but, on average, it systematically
underestimates the observed velocities by 13.3$\pm$10.0$\%$ for straight
fibers. For random orientation, the model has slightly higher deviations with
respect to the measurements and systematically overestimates them by
16.8$\pm$8.4$\%$. The better agreement between the maximum projection model
and the measurements is consistent with the observation that particles mostly
stabilize with their maximum projection area facing downward (SI Figures S1
and S2). However, even better agreement is found for the averaged orientation,
which is the arithmetic mean of the predictions for the maximum and random
orientations and allows for some oscillation around the maximum drag
orientation. With the average-orientation model, no systematic bias occurs and
the deviations are further reduced to 8.6$\pm$8.2$\%$. The results for
semicircular and quarter circular fibers are similar (SI Table S2).

The excellent agreement between the observed and modeled settling velocities
within less than 10$\%$ suggests that we can use the Bagheri and Bonadonna
(2016) 24 scheme with averaged orientation to realistically simulate
gravitational settling in the atmosphere. To explore the effects of the shape
dependence of gravitational settling on the global transport of microplastics
in the atmosphere, we therefore implemented this scheme into the Lagrangian
atmospheric transport model, FLEXPART 32, 33 (SI Table S3).

With the extended model, we performed 1-year simulations of particle transport
in the atmosphere for spheres as well as for straight fibers with aspect
ratios of 20, 50, and 100. All particles had the same volume, corresponding to
an equivalent sphere with a diameter of $75\text{\,}\mathrm{\SIUnitSymbolMicro
m}$, which can be considered as giant particles 5, 6. We ran two types of
simulations: in the first set of simulations, we released particles in
instantaneous pulses 10-100 m above the ground once per day at local noon from
five release points to gather statistical information about their atmospheric
lifetimes and transport distances. In the second set of simulations, we used a
realistic scenario of land-based microplastic emissions and explored the
resulting global atmospheric concentration and deposition patterns for spheres
and fibers (see Methods).

The deposition patterns resulting from the first set of simulations clearly
show that the atmospheric transport distances depend systematically on the
particle shape (Figure 2 and SI Figure S5). For instance, for a release point
in northern Italy, for spheres virtually all deposition occurs in central and
southern Europe, whereas straight fibers with AR $=100$ are also deposited in
northern Africa and northern Europe and small amounts even reach the Arctic
(SI Figure S6a-d).

Figure 3: Characteristics of microplastics transport in the atmosphere. Shown
are FLEXPART model simulation results for three release points (northern
Italy; Shanghai, China; southwest Pacific) and for microplastic particles with
an equivalent diameter of $75\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for
spheres (pink) and straight fibers with an aspect ratio of 100 (blue). (a)
Shown on the map is the annual mean total deposition from the atmosphere for
spheres and fibers. (b) Annual mean values of the horizontal transport
distances (colored bars) and their standard deviation (whiskers) for spheres
and fibers released from the three points. (c) Decrease of the atmospheric
microplastic burden as a function of time after release of spheres and fibers
from the three points, with the solid lines showing the median values and the
shading indicating the range between the 25th and 75th percentiles.

On average across our five release points, the mean atmospheric transport
distances of fibers with aspect ratios of 20, 50, and 100 are, respectively,
157$\pm$26%, 272$\pm$50%, and 394$\pm$79% greater than for spheres with the
same volume (SI Figure S5). This is a result of the longer residence time of
fibers in the atmosphere compared to spheres, with e-folding times of 2.4,
4.1, 4.6, and 5.3 hours for spheres and straight fibers with aspect ratios of
20, 50, and 100, respectively. Consequently, the median fractions of their
emitted mass residing in the atmosphere differ by orders of magnitude after a
few days (Figure 3c and SI Figure S7). The spread in the mass fraction
frequency distributions is also broader for fibers than for spheres,
indicating a strongly enhanced probability for very long range transport. This
explains why deposition and mass concentration fields extend over much larger
regions for fibers than for spheres (Figure 3a and SI Figures S6 and S8).

The second set of simulations shows that the deposition of spheres is strongly
focused on the densely populated source regions, while fibers are deposited
globally (Figure 4a,b and SI Figure S9a-d). For the fibers with AR $=100$,
only remote regions in the south Pacific and interior Antarctica remain nearly
unaffected by microplastic deposition.

For example, our simulations show a total deposition of 2.4 t/year in the high
Arctic (north of 75°N) for fibers with AR $=100$, while volume equivalent
spheres do not reach this region at all (SI Table S4). Our results explain why
the high Arctic, despite its remoteness, has been reported to be heavily
affected by microplastic deposition from the atmosphere 34, 17, and why most
of the microplastic particles found there appear to be fibers34.

Many studies discuss the impact of microplastic on the World Ocean 35, 36, 37,
however, the contribution of atmospheric transport to microplastic ocean
contamination remains unknown. Our simulations show that if all particles are
shaped like spheres, 16 kt/year are deposited in the oceans, whereas for
straight fibers with aspect ratios of 20, 50, and 100, the corresponding
numbers are 18, 20, and 23 kt/year, respectively. Furthermore, spheres are
deposited mainly in coastal regions close to population centers, whereas the
straight fibers also reach remote ocean areas. For the remote central Indian
Ocean (SI Figure S2), $\sim$7 times more microplastic mass would be deposited
if particles are shaped as fibers with AR $=100$ than if they are spheres (SI
Table S4).

Remote land regions are also contaminated more severely for fibers than for
spheres, as shown in Figure 4a,b. For instance, the interior of Australia (SI
Figure S2) receives 90$\%$ more microplastic mass for fibers with AR$=100$
than for spheres. These results are in good agreement with the fact that in
relatively remote regions, such as national parks, mainly microplastic fibers
and other non-spherical particles have been reported 20, 21, 22, 23, 18, 19,
17, whereas reports of microplastic spheres are less common.

The simulated vertical distribution of microplastic particles in the
atmosphere is also very different for spheres and straight fibers (Figure
4c,d), with the fibers reaching much higher altitudes than spheres. For
instance, the microplastic mass at altitudes greater than 4 km above the
surface is 5.5, 9.0, and 13.3 times higher for straight fibers with AR $=20$,
AR $=50$, and AR $=100$, respectively, than for spheres (SI Figure S9e-h). The
effective transport of fibers to high altitudes could have substantial
implications for ice cloud formation, since microplastic particles are thought
to serve as ice nuclei 38. The larger surface area of fibers compared to that
of spheres of the same volume is another important factor, possibly making
microplastic fibers highly effective ice nuclei with an impact on climate.

Figure 4: Shape dependence of global microplastic deposition and vertical
distribution in the atmosphere. Shown are results for particles with an
equivalent diameter of $75\text{\,}\mathrm{\SIUnitSymbolMicro m}$ that only
deviate in their shape, for (a) spheres and (b) straight fibers with an aspect
ratio of 100. Zonal median atmospheric mass concentration of microplastic as a
function of latitude and altitude for (c) spheres and (d) straight fibers with
an aspect ratio of 100.

It seems even likely that microplastic fibers of smaller sizes can reach the
stratosphere, with potentially severe consequences for the ozone layer. For
fibers with AR $=100$ and a density of
$900\text{\,}\mathrm{kg}\text{\,}{\mathrm{m}}^{-3}$, typical of polyurethane
(density of $1400\text{\,}\mathrm{kg}\text{\,}{\mathrm{m}}^{-3}$, typical of
polyvinyl chloride), we obtain settling velocities of less than 0.2 mm/s at
stratospheric altitudes between 20 and 30 km for fiber lengths of
$94\text{\,}\mathrm{\SIUnitSymbolMicro m}$
($75\text{\,}\mathrm{\SIUnitSymbolMicro m}$). This is slower than the minimum
mean upwelling velocity of the Brewer-Dobson circulation near the tropical
tropopause 39, 40, leading to the fibers’ ascent into the stratosphere, where
removal processes such as gravitational settling, chemical degradation or
incorporation into polar stratospheric clouds are not effective and can take
years for the particle sizes mentioned. Many plastic products contain bromine
or chlorine, for instance as flame retardants 41, and polyvinyl chloride
consists of more than 50% chlorine by weight. Plastics degrade under exposure
to ultraviolet (UV) light and can release halogen-containing gases 42. Their
large surface area compared to their volume, the horizontal orientation of
their maximum projection area, and long residence times of possibly years,
make a complete disintegration of halogen-containing fibers exposed to the
extreme UV levels in the stratosphere seem plausible. The released bromine and
chlorine compounds could participate in the catalytic destruction of ozone,
similar to those released from the chlorofluorocarbons and halons regulated by
the Montreal Protocol.

We have shown that the shape of microplastics is an important factor for their
global presence in the environment: the more non-spherical their shape, the
larger their horizontal and vertical transport range. Our findings demonstrate
that microplastics can be transported in the atmosphere to almost any point of
the globe and are present throughout the troposphere and possibly the
stratosphere. Novel laboratory experiments and model analyses carried out here
diminish uncertainties regarding the settling behavior of fibers in the
atmosphere, leading to more accurate model simulations of atmospheric
concentration and deposition patterns. The slow settling velocities obtained
for fibers make it also seem plausible that microplastic fibers can reach the
stratosphere, where they might endanger the ozone layer. Moreover, particles
of other shapes than straight or bent fibers, such as films 23, 18 or
particles with non-smooth surface textures, may have an even larger
atmospheric transport potential. However, currently both the shape and size
distribution of nano- and microplastic particles are largely unknown and more
research is needed for their characterization.

###  1.1 Acknowledgements

We thank Constanza Bonadonna for establishing contacts between our groups. We
acknowledge support from the University of Vienna’s research platform PLENTY
(Plastics in the Environment and Society). TB was funded by the German
Research Foundation (DFG) Walter Benjamin Position (project no. 463393443). JG
was supported by funding from the European Union Horizon 2020 Research and
Innovation Programme under the Marie Sklodowska-Curie Actions, Grant Agreement
No.675675. LB was funded by the Austrian Science Fund in the framework of the
project P 34170-N, ”A demonstration of a Lagrangian re-analysis (LARA)”. We
further thank Katharina Baier, Marina Dütsch, Blaz Gasparini, Lukas Kugler,
Andreas Plach, Johannes Seezing, Andrey Skorokhod, and Martin Vojta for their
support.

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# DexArt: Benchmarking Generalizable Dexterous Manipulation with
Articulated Objects

Chen Bao1* Helin Xu2* Yuzhe Qin3 Xiaolong Wang3
1Shanghai Jiao Tong University 2Tsinghua University 3UC San Diego

###### Abstract

To enable general-purpose robots, we will require the robot to operate daily
articulated objects as humans do. Current robot manipulation has heavily
relied on using a parallel gripper, which restricts the robot to a limited set
of objects. On the other hand, operating with a multi-finger robot hand will
allow better approximation to human behavior and enable the robot to operate
on diverse articulated objects. To this end, we propose a new benchmark called
DexArt, which involves Dexterous manipulation with Articulated objects in a
physical simulator. In our benchmark, we define multiple complex manipulation
tasks, and the robot hand will need to manipulate diverse articulated objects
within each task. Our main focus is to evaluate the generalizability of the
learned policy on unseen articulated objects. This is very challenging given
the high degrees of freedom of both hands and objects. We use Reinforcement
Learning with 3D representation learning to achieve generalization. Through
extensive studies, we provide new insights into how 3D representation learning
affects decision making in RL with 3D point cloud inputs. More details can be
found at https://www.chenbao.tech/dexart/.

Figure 1:  Overview. (a) We propose DexArt, a task suite of Dexterous
manipulation with Articulated object using point cloud observation. (b) We
experiment with extensive benchmark methods that learn category-level
manipulation policy on seen objects. (c) We evaluate the policies’
generalizability on a collection of unseen objects, as well as their
robustness to camera viewpoint change.

**footnotetext: Equal contributions. Work done while interning at UC San
Diego.

##  1 Introduction

Most tools and objects humans interact with are articulated objects. To allow
household robots to facilitate our daily life, we will need to enable them to
manipulate diverse articulated objects with multi-finger hands as humans do.
However, learning dexterous manipulation remains a challenging task given the
high Degree-of-Freedom (DoF) joints of the robot hands. While recent work has
shown encouraging progress in using Reinforcement Learning (RL) [69, 29, 1, 8]
for dexterous manipulation, most research focuses on manipulating a single
rigid object. The manipulation of diverse articulated objects not only adds
additional complexity with joint DoF, but also brings new challenges in
generalizing to unseen objects in test time, which has been a major bottleneck
for RL. This requires efforts on integrating 3D visual understanding and robot
learning on a novel benchmark.

Recent proposed robotic manipulation benchmarks [65, 12, 7, 34] play important
roles in robot learning algorithm development. For example, the MetaWorld [65]
benchmark provides more than 50 tasks for evaluating RL algorithms. However,
each proposed MetaWorld task only focuses on one single object without
considering generalization across object instances. To enable generalizability
for the robots, the ManiSkill [41, 19] benchmark is proposed with diverse
manipulation tasks and a large number of objects to manipulate within each
task. While this is encouraging, the use of a parallel gripper has limited the
tasks the robot can perform, and the ways how the robot can operate. For
example, it is very challenging for a parallel gripper to pick up a bucket
using the handle.

In this paper, we propose a new benchmark for Dexterous manipulation with
diverse Articulated objects (DexArt). We introduce multiple tasks with a
dexterous hand (the Allegro Hand) manipulating the articulated objects in the
simulation. For each task, instead of operating with a particular object, we
provide a training set of diverse articulated objects and the goal is to
generalize the policy to a different test set of articulated objects. To
achieve such a generalization, we incorporate RL with generalizable visual
representation learning: we adopt 3D point clouds as our observations and use
a PointNet encoder [44] to extract visual representations for decision making.
The generalizability of the policy depends on the 3D structure understanding
modeled by the PointNet encoder. We experiment and benchmark with different
methods and settings, and provide four key observations as follows:

(i) Training with more objects leads to better generalization. For each task,
we trained policies using varying numbers of objects for each task and tested
them on the same set of unseen objects. We find training with more objects
consistently achieves better success rates. Similar findings have been
reported in studies on manipulation with parallel grippers (Generalist-
Specialist Learning [24], ManiSkill [41]). While this might not be surprising
from the perception perspective, it does present more challenges for a single
RL policy to work with different objects simultaneously. It highlights the
importance of learning generalizable visual representations for RL.

(ii) Encoder with a larger capacity does not necessarily help. We experiment
with different sizes of PointNet encoders, and we observe the simplest one
with the least parameters achieves the best sample efficiency and success
rate, whether the network is pre-trained or not. This is surprising from the
vision perspective, but it is consistent with previous literature which shows
RL optimization becomes much more challenging with large encoders [41].

(iii) Object part reasoning is essential. With multi-finger hand interacting
with different object parts, our intuition is that object part recognition and
reasoning can be essential for manipulation. To validate our intuition, we
pre-train the PointNet encoder with object part segmentation tasks. We show
the object part pre-training can significantly improve sample efficiency and
success rate compared to approaches without pre-training and with other pre-
training methods.

(iv) Geometric representation learning brings robust policy. We evaluate the
robustness of the policy under unseen camera poses. We find that the policy
trained with partial point cloud is surprisingly resilient to variations in
camera poses, which aligns with the previous studies that use complete point
clouds in policies [32]. The accuracy remains consistent even with large
viewpoint variation. This is particularly useful for real robot applications
as it is challenging to align the camera between sim and real.

With the proposed baselines and detailed analysis among them, we hope DexArt
benchmark provides a platform to not only study generalizable dexterous
manipulation skill itself, but also study how visual perception can be
improved to aim for better decision making. We believe the unification of
perception and action, and studying them under DexArt can create a lot of
research opportunities.

##  2 Related Work

Dexterous Manipulation. Dexterous manipulation with multi-fingered robotic
hands has been a long standing problem in robotics. Previous methods formulate
dexterous manipulation as a planning problem [21, 51, 43, 3, 5, 13] and solve
it with trajectory optimization [28, 39, 58]. These methods require well-tuned
dynamics model for the robot and the manipulated object, which limits their
generalizability. On the other hand, data-driven-based methods do not assume a
pre-built model. The policies are learned either from demonstrations using
imitation learning [48, 20, 68, 50, 26, 49, 10, 63] or from interaction data
using reinforcement learning [29, 1, 69, 8, 23]. However, most methods focus
on tasks with single-body objects like grasping or in-hand manipulation.
Dexterous manipulation on articulated objects remains a challenging problem.
In this paper, we propose a new benchmark on learning generalizable
manipulation policy on articulated objects with point cloud observations.

Articulated Object Manipulation. The ability to perceive and manipulate
articulated objects is of vital significance for domestic robot. There have
been a lot of recent advancement on perception of articulated objects such as
pose estimation and tracking [57, 30, 33], joint parameter prediction [40, 56,
67, 25], part segmentation [38, 64, 15], and dynamics property estimation
[22]. On the robotics side, previous works [11, 52] also explore model-based
control and planning for articulated object. A natural extension is to combine
both lines of research by first estimating the articulated object model with
perception algorithm and then manipulating it with model-based control [35,
59]. Another line of research bypasses the state and model estimation by
directly learning the actionable information from raw sensory input [36, 62].
However, these approaches define a single-step action representation and
execute it with pre-defined controllers in an open-loop manner. Different from
these approaches, we formulate articulated object manipulation as a sequential
decision making process where visual feedback is used in closed-loop control.
During policy learning, we also study how 3D articulated object representation
learning can help decision making.

Learning from Point Clouds. Point cloud learning has been a long-last research
topic in 3D vision. The pioneer architectures for point cloud, e.g. PointNet
[44, 45], SSCNs [18] have been widely used for geometric representation
learning in part segmentation [38, 64, 15] and 3D reconstruction [25, 15]
tasks. In robotics, the learned point cloud representation also facilities
down-stream manipulation tasks, e.g. grasp proposal [55, 46, 6, 31],
manipulation affordance [37, 36, 27], and key points [16]. Recently,
researchers have explored to use point cloud as the direct input observation
for RL policy [8, 23, 60, 41]. Inspired by these works, our DexArt benchmark
introduces new tasks using a multi-finger hand to operate articulated objects.
It is more challenging compared to previous environments given the high DoF
for both the manipulator and the object. To tackle these tasks, we perform
extensive experiments on how geometric representation learning (e.g., part
reasoning) can affect decision making, which has not been thoroughly studied
before.

##  3 DexArt Benchmark

We propose the DexArt benchmark which contains tasks with different levels of
difficulty. It can be used to evaluate the sample efficiency and
generalizability of different policy learning methods. In this work, we
provide four dexterous manipulation tasks, Faucet, Bucket, Laptop and Toilet,
each with a number of seen and unseen objects (see Table 1).

###  3.1 Task Description

Faucet. As shown in the first row of Figure 1, a robot is required to turn on
a faucet with a revolute joint. The robot hand needs to firmly grasp the
handle and then rotate it by around 90 degrees. This task evaluates the
coordination between the motion of both dexterous hand and arm. While a 2-jaw
parallel gripper can potentially perform this task, it heavily relies on
precise arm motion due to its low DoF end-effector. The evaluation criteria
are based on the rotated angle of the handle.

Task | objects
---|---
| All | Seen | Unseen
Faucet | 18 | 11 | 7
Bucket | 19 | 11 | 8
Laptop | 17 | 11 | 6
Toilet | 28 | 17 | 11
Table 1: Task Statistics.

Figure 2: Tasks and Dexterous Hand. Left: visualization for all four tasks in
DexArt Benchmark. Right: visualization of Allegro hand where red arrows
indicate the revolute joint positions.

Bucket. As shown in the second row of Figure 1, this task requires the robot
to lift a bucket up. To ensure stable lifting behavior, the robot should
stretch out its hand under the bucket handle and hold it to construct a form
closure [4]. On the contrary, a single parallel gripper can only grasp it with
force closure [2], which can hardly achieve success without sufficiently large
friction. In evaluation, this task is considered a success if the bucket is
lifted to a given height.

Laptop. As shown in the third row of Figure 1, in this task, a robot should
grasp the middle of the screen and then open the laptop lid. This task also
fits dexterous hand well. A parallel gripper can do this by precisely plugging
the lid between its jaws. However, this constraint increases the difficulty
for arm motion and requires a larger workspace to open the lid. This task is
evaluated based on the changed angle of laptop lid.

Toilet. As shown in the fourth row of Figure 1, the task is similar to the
Laptop task, where the robot needs to open a larger toilet lid. The task is
harder as the geometry of the lid is more irregular and diverse. The task is
successfully solved if the toilet lid is opened at a threshold degree.

###  3.2 Environment Setup

In our benchmark, we implement our tasks in SAPIEN physical simulator [61]
using a XArm6 robot arm (6 DoF) with an anthropomorphic hand, Allegro Hand (16
DoF).

Preliminaries. We model our control problem with dexterous hand as a Markov
Decision Process (MDP),
$\mathcal{M}=\\{\mathcal{S},\mathcal{A},\mathcal{R},\mathcal{T},\rho_{0},\gamma\\}$,
where $\mathcal{S}\in\mathbb{R}^{n}$, $\mathcal{A}\in\mathbb{R}^{m}$ stand for
state and actions respectively.
$\mathcal{R}:\mathcal{S}\times\mathcal{A}\to\mathbb{R}$ is the reward function
that measures the task progress, where human knowledge is often incorporated
to guide the accomplishment of challenging tasks.
$\mathcal{T}:\mathcal{S}\times\mathcal{A}\to\mathcal{S}$ is the transition
dynamics. $\rho_{0}$ is the initial probability distribution and
$\gamma\in[0,1)$ is the discount factor.

Observation Space. The observation consists of two parts. First, the
proprioceptive data $S_{r}$ includes the current joint position of the whole
robot, linear velocity, angular velocity, position and pose of the end-
effector palm. Second, the partial point cloud $P_{o}$ captured by a depth
camera includes the articulated object and the robot. The observed point cloud
is first cropped within the robot workspace and then down-sampled uniformly.
We also concatenate the observed point cloud $P_{o}$ with an imaged robot
point cloud $P_{i}$ (see Section 4.1). All these observations are easily
accessible for real-world robots and no oracle information is used.

Action Space. The action is a 22-dimensional vector that consists of two
parts, 6-DoF for arm and 16-DoF for hand. We use an operational space control
for robot arm where the first 6-D vector is the target linear and angular
velocity of the palm. For Allegro hand, we use a joint position controller to
command the position target of 16 joints. Both controllers are implemented by
PD control.

###  3.3 Reward Design

The reward design for all dexterous manipulation tasks follows three
principles. (i) To ensure each task is solvable in a reasonable amount of
time, a dense reward is required. (ii) To eliminate unexpected behavior, the
reward should regulate the behavior of policy to be natural (human-like) and
safe. (iii) The reward structure should be general and standardized across all
tasks. We decompose our tasks into three stages: reaching the functional part,
constructing contact between the hand and manipulated objects, and executing
task-specific actions to move the manipulated parts.

Reaching and Grasping Stage. We design a reach reward for the first two stages
to encourage the robot hand to get close to the manipulated object as follows:

$\vspace{-1em}r_{\text{reach}}=\textbf{1}(\text{stage ==
1})\min(-\|\textbf{x}_{\text{palm}}-\textbf{x}_{\text{object}}\|,\lambda),$
(1)

where 1() is an indicator function, $\textbf{x}_{\text{palm}}$ and
$\textbf{x}_{\text{object}}$ is the 3D position of palm and object in the
world frame, $\lambda$ is a regularization term to prevent sudden surge in
reward. Equation 1 only considers the Cartesian distance between hand and
object, which may cause unexpected behavior, e.g., opening the laptop lid with
a clenched motion rather pushing the side of the lid with hand. In the real
world, such motion may cause damage to the manipulated object and robot
itself. Inspired by [47], we add a contact term to encourage better contact
between fingers and object:

$\displaystyle r_{\text{contact}}=\textbf{1}(\text{stage}\geq 2)\text{
IsContact }\left(\text{ palm, object }\right)$
$\displaystyle\textbf{AND}\left(\sum_{\text{finger }}\text{ IsContact }(\text{
finger, object })\geq 2\right),$ (2)

where IsContact is a boolean function that performs collision detection to
check whether two links are in contact. We believe a good contact relationship
is constructed if both the palm and at least two fingers touch the object.

Part Manipulation Stage. In the last stage, the robot needs to manipulate the
specific part of an articulated object to move it to the given pose. The
reward of this stage is designed as follows:

$\displaystyle r_{\text{progress}}=\textbf{1}(\text{stage ==
3})\text{Progress(task),}$ (3)

where Progress is a task-specific evaluation function for the current task
progress. For example, in the Faucet environment, we use the change of handle
joint angle to indicate task progress.

To eliminate jerky and unstable robot motion, we add a penalty term
$r_{\textrm{penalty}}$, which includes a L2 norm of the action and a task-
specific term. The overall reward is the weighted sum of four reward terms.
More details on the reward design can be found in our supplementary material.

Figure 3: Overview. We adopt PPO algorithm with PointNet backbone to learn
dexterous manipulation on articulated objects. We use pre-training to
facilitate the policy learning process. (1) The PointNet is pre-trained on
perception-only tasks, which includes segmentation, reconstruction, SimSiam,
etc. (2) The pre-trained PointNet weight is then used to initialize the visual
backbone in PPO before RL training.

###  3.4 Asset Selection and Annotation

We use the articulated object models from the PartNet-Mobility [61] dataset.
We manually select object models for each task to avoid bad modeling and to
ensure a consistent kinematics structure. We further annotate the scale and
initial positions object-by-object to make sure they have reasonable sizes and
don’t initially intersect with the robot. We further apply randomness to the
object initial position, i.e. for each task, we perform reasonable rotation
and translation from the annotated position while making sure the goal is
still achievable, and the object is randomized from the training set during
policy learning.

##  4 Method

Solving dexterous manipulation tasks with RL methods suffers from high sample
complexity due to high-dimensional action space. Tasks with articulated
objects and point cloud observation increase the complexity further. In this
section, we will discuss several methods for improving policy learning
performance. In Section 4.1, we will talk about the policy learning
architecture. Section 4.2 will describe details on how to generate the data
for visual pre-training. Finally, we will discuss the pre-training methods
evaluated in our benchmark in Section 4.3.

###  4.1 Policy Overview

Policy Learning. To achieve category-level generalization across diverse
objects, we adopt 3D point cloud as our observation and use Proximal Policy
Optimization (PPO) [53] as our RL algorithm. In the architecture design, the
value and policy networks share the same feature extracted from the point
cloud and robot proprioception, as shown in the right part of Figure 3. We use
PointNet [44] as the point cloud feature extractor. It is worth noting that we
employ a simple version of PointNet. The local MLP has one hidden layer with a
GELU activation function, followed by a max pooling that directly produces the
output feature $F_{1}$. Meanwhile, an MLP is used to extract output feature
$F_{2}$ from the robot proprioception vector $S_{r}$. The output feature
$F_{1}$ and $F_{2}$ are then concatenated and passed through the value MLP and
policy MLP. We show in experiments that increasing the volume of the vision
extractor actually harms policy learning.

Feature Extractor Pre-training. We investigate how 3D representation learning
helps with 3D policy learning. We benchmark vision pre-training with five
different 3D representation learning methods, including both self-supervised
learning and supervised learning, which will be discussed in Section 4.3. For
all methods, we pre-train a visual model with PointNet backbone on perception-
only tasks, and then use it to initialize the feature extractor for RL. The
pre-training pipeline is illustrated in Figure 3.

Point Cloud Imagination. The point cloud RL has two challenges. First, the
hand-object interaction will cause several occlusions. Second, the RL training
can only handle low-resolution point cloud due to the memory limitation. Thus
only few points in the observation come from the hand fingers, which is
essential information for decision making. Inspired by [47], we leverage the
robot model to compute the finger geometry via forward kinematics. We can then
sample points $P_{i}$, called imagined point cloud, from the computed
geometry. As shown in the right part of Figure 3, our point cloud feature
extractor takes as input both observed points $P_{o}$ and the imagined points
$P_{i}$ (deep-colored points in Figure 3). This way, we provide the missing
details of the robot in point cloud observation. Note that $P_{i}$ is
accessible even for real robot.

Task | Faucet | Bucket | Laptop | Toilet
---|---|---|---|---
Split | Seen | Unseen | Seen | Unseen | Seen | Unseen | Seen | Unseen
No Pre-train | $0.30\pm 0.22$ | $0.28\pm 0.21$ | $0.51\pm 0.12$ | $0.56\pm 0.08$ | $0.81\pm 0.01$ | $0.41\pm 0.09$ | $0.71\pm 0.05$ | $0.46\pm 0.02$
Segmentation on PMM | $0.27\pm 0.12$ | $0.17\pm 0.09$ | $0.35\pm 0.25$ | $0.34\pm 0.24$ | $0.85\pm 0.09$ | $0.55\pm 0.09$ | $0.66\pm 0.08$ | $0.44\pm 0.02$
Classification on PMM | $0.20\pm 0.12$ | $0.18\pm 0.14$ | $0.56\pm 0.06$ | $0.58\pm 0.12$ | $0.80\pm 0.20$ | $0.41\pm 0.14$ | $0.69\pm 0.08$ | $0.38\pm 0.03$
Reconstruction on DAM | $0.35\pm 0.02$ | $0.21\pm 0.03$ | $0.51\pm 0.08$ | $0.50\pm 0.05$ | $0.85\pm 0.04$ | $0.54\pm 0.08$ | $0.76\pm 0.03$ | $0.52\pm 0.03$
SimSiam on DAM | $0.60\pm 0.15$ | $0.45\pm 0.12$ | $0.41\pm 0.30$ | $0.38\pm 0.31$ | $0.84\pm 0.04$ | $0.49\pm 0.13$ | $0.82\pm 0.02$ | $0.50\pm 0.06$
Segmentation on DAM | $\mathbf{0.79\pm 0.02}$ | $\mathbf{0.58\pm 0.07}$ | $\mathbf{0.75\pm 0.04}$ | $\mathbf{0.76\pm 0.07}$ | $\mathbf{0.92\pm 0.02}$ | $\mathbf{0.60\pm 0.07}$ | $\mathbf{0.85\pm 0.01}$ | $\mathbf{0.55\pm 0.01}$

Table 2: Success Rate of Different Pre-training Methods. We report the success
rate (mean $\pm$ std) on four tasks, for both seen and unseen objects. DAM =
DexArt Manipulation Dataset, PMM = PartNet-Mobility Manipulation Dataset, as
described in section 4.2.  Figure 4: Pre-training Visualizations. We visualize
the segmentation and reconstruction pre-training results on Toilet (top row)
and Faucet (bottom row).

###  4.2 Pre-training Datasets

DexArt Manipulation Dataset (DAM). We render the point cloud observations with
the setting as manipulation tasks. The dataset contains 6k point clouds for
each object, including observed and imagined points, where the state of robot
and articulated object are sampled randomly, as shown in the left column of
Figure 4. For segmentation pre-training, we label the point cloud into 4
groups: the functional part of the object, the rest of the object, the robot
hand, and the robot arm, as shown in the middle column of Figure 4.

PartNet-Mobility Manipulation Dataset (PMM). Different from DAM, PMM is
directly rendered from PartNet-Mobility [61] without task information, e.g.
robot. PMM contains 46 object categories and 1k point clouds for each
category. The state of the object and the camera viewpoint are sampled
randomly. For classification, each object in the same category shares the same
label. For segmentation, we follow the procedure in [17] to generate ground
truth segmentation masks for functional parts on the articulated objects.

Figure 5: Segmentation After RL Tuning. We visualize the segmentation results
after the PointNet is tuned during policy learning. The weight from PPO point
cloud feature extractor can be directly applied back to the segmentation
network to perform segmentation prediction. Figure 6: Training Process with
Different Number of Seen Objects. The x-axis is the environment steps. The
y-axis of the upper row is the success rate on unseen objects, evaluated with
3 random seeds, and the shaded area indicates standard deviation. The y-axis
of the bottom row is the episodic return, where the shaded area represents the
standard error. The grey curves show methods with segmentation pre-training on
around 50% of the seen DexArt objects within each category, compared with the
red curves that are pre-trained with 100%. Figure 7: Training with Different
PointNet Sizes. The axes mean the same as in Figure 6. The experiments with
tree curves are segmentation pre-trained on DAM(100%), with small/medium/large
PointNet described in Section 5.2.

###  4.3 Pre-training Methods

Supervised Pre-training. We experiment with two supervised pre-training
methods including semantic segmentation and classification. For
classification, we train a PointNet on PMM data to predict the label for 46
object categories. Compared to simpler tasks like grasping, articulated object
manipulation requires more understanding on 3D parts. The policy needs to
locate the functional part and reason how to interact with it. Thus, we also
investigate how pre-training on part segmentation can help policy learning. We
train segmentation on both DAM and PMM.

Self-supervised Pre-training. We also experiment with two self-supervised pre-
training methods, including point cloud reconstruction and SimSiam [9].
Following OcCo [54], we use an encoder-decoder architecture for point cloud
reconstruction on DAM dataset. The encoder is a PointNet that extracts global
embedding and the decoder is a PCN [66] which reconstructs the original point
cloud from global embedding. The reconstruction is trained via Chamfer loss
[14]. The reconstruction results are visualized in the right column of Figure
4. After pre-training, we use the PointNet encoder to initialize the PointNet
in PPO.

We follow SimSiam and design a siamese network with PointNet. In SimSiam
training, the network takes two augmented views of the same point cloud, and
forwards them into the same PointNet encoder. An MLP is connected on one side
to predict the similarity while the gradient is stopped on the other side. The
method is trained to maximize the similarity between both sides. We pre-train
the PointNet encoder inside SimSiam on the DAM dataset.

##  5 Experiment

We conduct experiments on the proposed tasks including Faucet, Bucket, Laptop,
and Toilet defined in Section 3.1. We perform experiments on three aspects:
(i) We benchmark different pre-training methods by evaluating both seen and
unseen articulated objects for all tasks. We test the success rate during and
after training. (ii) We ablate how the number of seen objects and the
architecture size of visual backbone can affect policy learning. (iii) We
study the robustness to camera viewpoint change for different methods, where
we evaluate the task success rate when the input point cloud is captured by
cameras at novel poses. Overall, we evaluate the methods by success rate and
episodic returns on both seen objects and unseen objects. We train RL policy
with 3 different random seeds for each experiment.

###  5.1 Main Results

We provide the success rates of all benchmark methods in Table 2. We compare
the RL policy trained from scratch (1st row) with five different pre-training
methods (the following rows). The results show that proper visual pre-training
can benefit the policy learning. We highlight our findings as follows. (i)
Part segmentation boosts the policy learning on all tasks. It performs the
best on all tasks. With segmentation pre-training, the PointNet can better
distinguish and locate the functional parts, which is critical for articulated
object manipulation. (ii) Other pre-training methods to learn a representative
global embedding, i.e., classification, reconstruction, and SimSiam, also
improve the policy learning in some cases, especially on Laptop task. (iii)
Tasks that involve manipulating small functional parts, e.g. faucet handles,
benefit more from segmentation pre-training. As shown in Figure 8, the
segmentation results can predict the label of small faucet handles correctly,
while reconstruction focuses more on the global shape completeness and ignores
small part details. Thus, part segmentation is a more effective pre-training
method for more delicate manipulation tasks.

Figure 8: Different Pre-train Methods. Evaluation success rate of different
methods in Faucet and Bucket tasks. The shaded area indicates the standard
deviation.

###  5.2 Ablation Study

We ablate how the number of objects used in training, the size of the vision
extractor, and different visual representation learning methods influence the
generalizability.

Number of Seen Objects. Different from the previous experiment in Section 5.2,
we train our model and policy using only $50\%$ of the seen objects. We report
the learning curve and the success rate on novel objects during training for
methods using $50\%$ and $100\%$ of the objects. In Figure 6, while the
convergence speed (represented by episodic return) with 100% seen objects is
slower compared with the $50\%$ one due to more diverse object geometry, the
success rate (top row) of the $100\%$ training on unseen objects remains
higher during the whole training process and for all tasks. It demonstrates
more training objects are crucial for better policy generalizability.

Size of the Vision Extractor. We experiment with three different sizes for
PointNet: (i) The small PointNet with one hidden layer. (ii) The medium
PointNet with three hidden layers. (iii) The large PointNet with five hidden
layers. All other components for these three PointNet are the same.
Surprisingly, we find that the smallest PointNet achieves the best performance
for both success rate and episodic return, as shown in Figure 7. Different
from our common understanding from vision perspective, the smaller network not
only trains faster but also generalizes better.

Non-3D Representation. We compare our PointNet pre-trained on DAM segmentation
in Laptop task with following 2D pre-training representation : R3M[42].

Encoder | Seen | Unseen
---|---|---
PointNet | $0.78\pm 0.04$ | $0.41\pm 0.08$
ResNet-18 | $0.64\pm 0.07$ | $0.28\pm 0.05$
Table 3: Non-3D Representations.

In R3M, the Ego4D human video dataset was used to pre-train a ResNet-18 with
time-contrastive learning and video-language alignment. Table 3 shows the
results of the experiment. The results indicate that 3D visual representation
learning with PointNet is better at manipulating objects. Compared to Non-3D
representation learning, 3D policies can achieve better manipulation
performance on both seen and unseen objects.

###  5.3 Robustness to Viewpoint Change

We experiment with the viewpoint change of camera in Laptop task to evaluate
the robustness of policy based on PointNet and ResNet-18. The PointNet policy
is pre-trained on DAM segmentation and the ResNet-18 policy is pre-trained on
R3M. The viewpoint sampling procedure can be described as follow: (i)
Determine a semi-sphere for camera pose sampling. We first compute the radius
$r$ of the semi-sphere using the distance from the initial camera position to
the manipulated object. The center of this semi-sphere is defined by moving
along the camera optical line with distance $r$. (ii) Sample a point on the
semi-sphere as camera position. We uniformly sample the azimuthal angle in
every $20^{\circ}$ from $-60^{\circ}$ to $60^{\circ}$ and polar angle in every
$20^{\circ}$ from $-20^{\circ}$ to $20^{\circ}$, relative to the training
viewpoint. It results in $7\times 5=35$ camera positions in total. (iii)
Rotate the camera so that it points to the semi-sphere center. Using the
procedure above, we sample $35$ camera poses. We set these camera poses during
the inference.

As shown in Figure 9, the trained PointNet policy shows great robustness
against viewpoint change, even though we change the azimuthal angle by
$60^{\circ}$ and the polar angle by $20^{\circ}$. By contrast, the success
rate of the ResNet-18 policy suffers dramatically drop when the difference
between the training viewpoint and the novel evaluation viewpoint increases.
It informs us that the robustness mainly comes from point cloud representation
learning and PointNet architecture.

Figure 9: Success Rate under Different Viewpoints. The x-axis is the polar
angle $\phi$ (relative to the training viewpoint) and the y-axis is the
azimuthal angle $\theta$ on the semi-sphere centered at the object. The z-axis
represents the success rate. The viewpoint during training is highlighted by a
blue star.

##  6 Conclusion

We propose a new benchmark for dexterous manipulation with articulated
objects, and study the generalizability of the RL policy. We experiment and
benchmark with different methods to provide several insights: (i) RL with more
diverse objects leads to better generalizability. We find that training with
more objects leads to consistently better performance on unseen objects. (ii)
Large encoders may not be necessary for RL training to perform dexterous
manipulation tasks. We find that, in all environments, the simplest PointNet
always leads better sample efficiency and best generalizability. (iii) 3D
visual understanding helps policy learning. Part-segmentation facilities
manipulation with small functional parts while tasks with larger functional
parts benefit from all visual pre-training methods. (iv) Geometric
representation learning with PointNet feature extractor brings strong
robustness to the policy against camera viewpoint change. In conclusion, we
hope DexArt can serve as a platform to study generalizable dexterous
manipulation, and the joint improvement between perception and decision
making.

Acknowledgements. We thank Hao Su for providing valuable feedback to the
paper. This project was supported, in part, by the Industrial Technology
Innovation Program (20018112, Development of autonomous manipulation and
gripping technology using imitation learning based on visualtactile sensing)
funded by the Ministry of Trade Industry and Energy of the Republic of Korea,
Amazon Research Award and gifts from Qualcomm.

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