# Challenges and Outlook in Robotic Manipulation
of Deformable Objects

Jihong Zhu, Andrea Cherubini, Claire Dune, David Navarro-Alarcon, Farshid
Alambeigi, Dmitry Berenson, Fanny Ficuciello, Kensuke Harada, Jens Kober,
Xiang Li, Jia Pan, Wenzhen Yuan and Michael Gienger J. Zhu is with Cognitive
Robotics, TU Delft and Honda Research Institute, Europe<EMAIL_ADDRESS>Cherubini is with LIRMM - Université de Montpellier CNRS, 161 Rue Ada, 34090
Montpellier, France<EMAIL_ADDRESS>Dune is with COSMER
laboratory EA 7398, Universié de Toulon, 83130 La Garde, France.
<EMAIL_ADDRESS>Navarro-Alarcon is with The Hong Kong Polytechnic
University, Department of Mechanical Engineering, Kowloon, Hong Kong.
<EMAIL_ADDRESS>Alambeigi is with the University of Texas at Austin, Austin,
USA<EMAIL_ADDRESS>Berenson is with the University of
Michigan, Ann Arbor, MI, USA<EMAIL_ADDRESS>Ficuciello is with
Università degli Studi di Napoli Federico II, 80125 Napoli, Italy
<EMAIL_ADDRESS>Harada is with the Osaka University, Japan, and
the National Institute of AIST, Japan<EMAIL_ADDRESS>Kober is
with Cognitive Robotics, TU Delft, the Netherlands<EMAIL_ADDRESS>Li is
with Department of Automation, Tsinghua University, Beijing, China.
<EMAIL_ADDRESS>Pan is with with the Department of Computer Science,
The University of Hong Kong, Pok Fu Lam, Hong Kong<EMAIL_ADDRESS>Yuan is
with Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213 USA
<EMAIL_ADDRESS>Gienger is with Honda Research Institute Europe,
Offenbach, Germany<EMAIL_ADDRESS>work has been submitted to
the IEEE for possible publication. Copyright may be transferred without
notice, after which this version may no longer be accessible.

###### Abstract

Deformable object manipulation (DOM) is an emerging research problem in
robotics. The ability to manipulate deformable objects endows robots with
higher autonomy and promises new applications in the industrial, services, and
healthcare sectors. However, compared to rigid object manipulation, the
manipulation of deformable objects is considerably more complex, and is still
an open research problem. Addressing DOM challenges demand breakthroughs in
almost all aspects of robotics, namely hardware design, sensing, (deformation)
modeling, planning, and control. In this article, we review recent advances
and highlight the main challenges when considering deformation in each sub-
field. A particular focus of our paper lies in the discussions of these
challenges and proposing future directions of research.

##  I Introduction

Until now, object rigidity is one of the common assumptions in robotic
grasping and manipulation. Strictly speaking, all objects deform upon force
interaction. Rigidity is a valid assumption when object deformation can be
neglected in the task. Nevertheless, many objects that need to be manipulated
by robots present non-negligible deformation: from micro surgical operation to
challenging industrial assemblies.

Robots need to be capable of manipulating deformable objects to operate in
human environments. This capability would benefit many application fields,
while posing fundamental research challenges. In this article, we consider a
generalized concept of manipulation where grasping is also part of the task.
We will refer to the problem as deformable object manipulation (DOM).

The tasks involved in DOM cover a broad spectrum (see Fig. 1). These include:
dressing assistance in elderly care, cable harnessing in industrial
automation, harvesting and processing fruit and vegetables in agriculture,
surgical operations in medical services, to name a few.

Figure 1: Applications involving manipulation of deformable objects. Clockwise
from top left: dressing assistance [1], cable harnessing [2], fruit harvesting
[3], suturing [4]

On the technical side, addressing deformation introduces the following
technical challenges:

  * •

the complication of sensing deformation,

  * •

the high number of degrees of freedom of soft bodies,

  * •

the complexity of non-linearity in modeling deformation.

We believe that overcoming these challenges is not only beneficial to DOM, but
can further push towards developing autonomous robots which can operate in
unstructured environments.

Figure 2: A typical robotic framework for handling deformable objects. In this
particular example, the framework addresses wire harness [5].

In recent years, there have been a few surveys on robotic manipulation of
deformable objects. Some surveys focus on specific areas of DOM. The survey
from Jimenez [6] focuses on model-based manipulation planning. More recently,
Herguedas et al. [7] review works using multi-robot systems for DOM while the
work of [8] considers multi-modal sensing. The authors of [9] present the
state-of-the-art on deformable object modeling for manipulation. There are
also two comprehensive surveys in the area. The survey in [10] reviews and
classifies the state-of-the-art according to the object’s physical properties.
Lately, [11] reports most recent advances in modeling, learning, perception,
and control in DOM.

In contrast with the mentioned surveys, which either focus on reporting the
progress of the field or a specific area, this article aims at identifying
_scientific challenges_ introduced by object deformations and at projecting
crucial future research directions. As DOM is an emerging field of research
where there is still much to be done, in this paper, previous works and open
problems are given equal weights. In addition, we dedicate one section to
discussing practical challenges in various applications of DOM. We believe the
paper is a first of its kind, in the field of DOM.

A robotic framework designed to handle deformable objects usually consists of
five key components: _gripper and robot design_ , _sensing_ , _modeling_ ,
_planning_ and _control_ (See Fig. 2). To position the current research and
identify future trends, we conducted a survey on the future perspective of
deformable object manipulation111Link to the survey:
https://forms.gle/XCv2CV79yvRP5Gsd7. We shared the survey with people working
in related field, at various career stages. They were asked to rate the
importance and research maturity of each of the five identified key
components, from $1$ to $4$, with $1$ being not important/low maturity and $4$
being very important/high maturity. We received 31 answers that are summarized
on Fig. 3.

(a) Highest qualifications of the respondents.

(b) Means and variances of Importance and research maturity ratings of each
key component.

Figure 3: Summary of the outcomes of the survey on DOM. We received in total
$31$ answers. The respondents cover different level of qualifications ranging
from master students to full professors.

We consider the promising direction of research as the ones that have the
highest significance and the lowest research maturity. Based on the survey,
sensing is the most promising one among all subareas. This is probably due to
current booming trend in Deep Learning has offered many new methods for
processing the sensory data. In addition, sensing is the prerequisite for
subsequent steps such as modeling, planning and control.

Accordingly, the following sections of this paper each present one of these
five research directions. In each section, we review recent works in the field
and then comment the outlook and challenges ahead. Then, Sect. VII tries to
provide a link from research to practical applications in the context of DOM.
Finally, we summarize key messages in Sect. VIII.

##  II Gripper and robot design

###  II-A Current capability

Does manipulation of deformable objects demand specific grippers as compared
to manipulation of rigid objects? Generally, yes (see Fig. 4). Unlike rigid
objects (which are mostly handled by standard grippers), deformable objects
are handled with custom (and often designed ad-hoc) grippers, e.g. a 3D
printed gripper that enables cable sliding [5], a flat clip for holding towels
[12], a cylindrical tool for pushing and tapping plastic materials [13], a
soft hand for manipulating organs [14]. Such diversity in grippers is a result
of the large variety of deformable objects, which require different actions
during manipulation. To avoid designing task-specific grippers for DOM, human-
like dexterity and compliance is desired. Recent works in this directions
consider compliant design [15, 16] and show good potential for DOM tasks.

As for the robot itself, it is rigid in most works. In some cases, as in the
surgical application showcased in [17] (Fig. 4, bottom right), both robot and
object are deformable to ensure safety of manipulation.

Figure 4: Various robot grippers for DOM. Clockwise from top left: a tool for
pushing and tapping on plastic materials [13], flat clips for holding a towel
[12], a gripper allowing a cable to slide [5], a soft continuum manipulator
interacting with a deformable material [17] and a soft hand for manipulating
organs [14].

###  II-B Challenges and outlook

Improving dexterity is core to robot manipulation. The improvement can come
from different research domains, such as accurate in-hand sensing or robust
control, two aspects which we will detail in Sections III and VI,
respectively. In this section, our focus is on gripper/robot hardware aspects.

One way of achieving such dexterity is to reproduce by design the most
dexterous gripper – the human hand. An open question is whether
anthropomorphic design is in itself the optimal solution in all cases,
especially in the context of DOM.

While having one dexterous gripper which can handle a variety of DOM tasks is
appealing, it should be noted that additional constraints need to be
considered in the design process, for hygiene/safety in tasks such as food
handling or surgery. For instance, for surgical applications we are limited by
biocompatibility of the materials and actuators and by the reduced available
space in minimally invasive surgery. In theses cases, designing task-specific
grippers is more appropriate. Non-anthropomorphic soft grippers are another
emerging area of research [18]. These grippers are promising, to overcome the
challenges associated with traditional fingered grippers in grasping rigid
objects; yet, to date, their application to DOM receives little attention.

Otherwise, one may use a standard gripper, and provide the robot with suitable
tools to be grasped and used according to the type of task at stake. This
demands breakthroughs on the algorithmic side, to make the robot capable of
reasoning on the proper tools for different tasks. Training the robot to have
task-specific reasoning will enhance autonomy and make robots realize more
complex tasks.

(a) Picking raspberries [19].

(b) A custom 3D printed soft robotic gripper, grasping mushroom coral [20]

Figure 5: Two examples of interaction with fragile objects, which could
benefit from the use of soft robots.

Another area worth investigating is that of soft robots/grippers, since these
have great potential for manipulating fragile materials, such as organs or
food, or for collecting biological samples or fruits (see Fig. 5). While
traditional rigid robots need to exhibit compliant behavior when interacting
with these objects, the inherent compliance of soft robots makes the task
safe. This unconventional paradigm of using soft robots to manipulate soft
objects will bring new challenges in modeling and control as both the robot
and the object are under-actuated and difficult to model. One pioneering work
in this direction is [21], which adapts the finite element modeling (FEM)
based inverse soft robot model with contact handling (proposed in [22]) for
deformable objects manipulation using soft robots.

An interesting research question to consider is whether methods can be
transferred from one field to the other. To be more specific, can methods for
controlling/modeling soft robots be applied to manipulating deformable objects
and vice versa? If so, as a community, it may be valuable to obtain a unified
approach for working with both soft robots and deformable objects.

##  III Sensing

###  III-A Current capability

In this section, we consider visual, tactile and force sensing for DOM.
Existing research relies on these three modes to estimate the state of
deformable objects. In most cases, vision provides global information about
shapes on a large scale, while force and tactile provide local information on
both shape and contact. At the end of this section, we also discuss the
research in contrast with this common practice, where global deformation
properties are recovered using tactile sensing. It should also be noted that
force information is particularly important in industrial settings, e.g., for
assembly [23], [24]. Vision is used in tasks such as rope manipulation [25,
26] or cloth unfolding [27, 28], where the object exhibits large global
deformation. In these works, configurations of deformable objects were
obtained from raw image readings. Although vision offers a global perspective
of the object configuration, visual data can be noisy in unstructured
environments, it is then important to manage occlusions [12, 29]. Most of
above-mentioned works are based on 2D vision, 3D perception of deformable
objects is more challenging. Existing works employ FEM [30] or a combination
of Growing Neural Gas and Particle Graph Networks [31] for better tracking the
deformation. In a more recent study [32], it has been shown that a deep
convolutional neural network for processing vision data can be used with small
variations to process tactile data for deformable objects recognition.

Objects made of soft materials, such as human tissues and fruits, have a
special force-displacement correlation upon contact. As a result, tactile
sensing can be used to estimate the stiffness. In [33], the GelSight [34], a
vision-based high-resolution tactile sensor, measures the 3D geometry of the
contact surface, and the normal/shear forces.

Note that the division of vision for global deformation and tactile sensing
for local deformation is not absolute. The authors of [35] present to use
vision to estimate the local deformation of objects during grasping, and
classify objects accordingly. In [36], high-resolution tactile sensing is used
to estimate the physical properties of clothing materials through squeezing,
assuming the robot can learn from the data about indicating global properties
of clothing according to a local sampling point. In [37] an example of
servoing along a cable based on high-resolution tactile sensing is presented.
Although vision is not used, the precise measurement of the local cable shape
provides enough information to guide the robot motion on a small scale.

###  III-B Challenges and outlook

Here, the main challenges are: selecting appropriate sensors for the DOM task
and using the measurements to obtain meaningful object representations.

Considering the high number of degrees of freedom (DoF) of the deformable
bodies, fusion of different sensing modalities (vision, force and tactile) may
be a promising direction to pursue in future research.

Another research question to be answered is: what yields a good representation
of the object configuration? We (acknowledgedly) do not have a complete answer
to this; rather, we will elaborate on considerations when designing the
representation.

The representation need to be robust to noise and useful for reconstructing
the objects’ configuration – even when data are partially unavailable. In
vision, the most common noise is occlusion. How to generate a meaningful
representation of these objects under self occlusion is still an open problem
in research. For rigid objects, one can carefully design the environment to
avoid it. For deformable objects that exhibit large global deformation such as
clothes, bed sheets etc, self occlusion is inevitable during manipulation. A
promising direction to deal with occlusion and noise is using
active/interactive perception. With vision data from different perspectives,
we might be able to reconstruct the object’s configuration accurately even
under occlusion and noise.

Apart from the above mentioned challenges, choosing a good representation also
involves leveraging two aspects:

  1. 1.

the dimensionality of the representation,

  2. 2.

the accuracy of the representation.

Usually the trade-off depends on the task, relies on human intuition and
involves a trial and error process. In end-to-end reinforcement learning
settings, sensory data can be mapped directly to robot actions without
explicit feature representations [38]. Human demonstrations can be used for
making end-to-end learning more efficient. One example is reported in [39].
The authors use an improved version of Deep Deterministic Policy Gradients,
trained with $20$ demonstrations, to make robots manipulate cloth. However,
since such settings often require a manually designed cost/reward function for
learning, human demonstrations in this context can also be used for recovering
the reward, with inverse reinforcement learning.

##  IV Modeling

###  IV-A Current capability

For robots to perform deformation tasks using sensory data, we need a model
that captures the relationship between sensor information and robot motion. A
linear model characterized by Young’s modulus can be employed for describing
elastic deformation. The two other classes of deformation are: plastic, and
elasto-plastic deformations. This classification serves well. Yet, since the
model should be used for control, in this section, we prefer to distinguish
between local and global models – a taxonomy which has clearer implications
for control. We introduce the corresponding research and – at the end of the
section – we discuss the limitations of these models and present works that
address them.

Most local models approximate the perception/action relationship via a
Jacobian Matrix (called Interaction Matrix in visual servoing). Such a model
is linear and can be computed in real-time with a small amount of data. Yet,
since it is a local model, it should be continuously updated during task
execution. Model updating methods include: Broyden rule [17], receding horizon
adaption [40], local gradient descent [41], QP-based optimization [42], and
Multi-armed Bandit-based methods [43]. Another advantage of the Jacobian model
is that one can design a simple controller by inverting it. However, since
this controller is local, it should operate via a series of intermediate
target shapes [40], [42].

On the other hand, global models can be approximated with Finite Element
Methods [44] and also (deep) neural networks. In contrast to simple linear
models, (D)NN-based approaches benefit from stronger representation power, in
terms of accuracy and robustness [45]. Moreover, they can incorporate physics
models and reason about object interaction [46]. These models can approximate
highly nonlinear systems and have a larger validity range, solving (to some
extent) the locality issue of the linear models. Nevertheless, these complex
nonlinear representations demand large amounts of data (which might not be
available in some cases).

Yet, whether we use analytical or learned models, their predictive power will
be limited. They are either specialized to some class of tasks or learned from
a set of training data. Especially for the learned models, we can never hope
to collect enough data to produce an accurate model in the entire state space
(which is high dimensional). Thus [47] and [48] have developed methods to
reason about the validity of a (learned) model for a given state and action,
and have used these methods to reason about model uncertainty in planning and
control. However, when the model is not precise, a re-planning/recovery might
be desirable. The authors of [49] introduces two neural networks for learning
and re-planning the motion when the model is unreliable.

###  IV-B Challenges and outlook

The complexity of modeling is manifested in the lack of simulators. While most
existing robotic simulators are capable of producing rigid body kinematics and
dynamic behaviours, only a fraction of them can handle deformation. One recent
work, Softgym [50] was proposed for bench-marking DOM based on Nvidia Flex. In
the soft robotics community, SOFA [51] and Chainqueen [52] are example
simulators. In Sect. II-B, we considered the interaction between soft robots
and deformable objects. Thus, a unified simulator that is able to handle soft
robots and objects, and model their interaction might be desirable.

When choosing a model for control, one challenge of data-driven deformation
modeling is to balance region of validity with number of data required for
training. One possible direction is to combine a simple model with a complex
nonlinear model to form a hierarchical model. An example of such structures is
exploited in [53] for robust in-hand manipulation. For DOM tasks, we can have
a linear model at lower level, and a (D)NNs learning the full model at higher
level. The lower level model can be learned in few iterations to enable
instant interaction between robot and object. The higher level (D)NN can
collect data and improve the model to enhance global convergence.

##  V Planning

###  V-A Current capability

Planning aims at finding a sequence of valid (robot/object) configurations and
contributes to solving the problem of limited validity of local models, as
discussed in Sect. IV.

Planners can operate in the objects’ configuration space, and sometimes rely
heavily on physic-based simulation. While the obtained plan can be visually
plausible, it may be unrealizable for a specific object. Recently, McConachie
et. al. presented a framework which combines global planning without physics
simulation, with local control [54]. For an elastic object, considering its
energy is another way to do planning; in this direction, Ramirez-Alpizar et
al. [55] proposed a dual-arm manipulation planner optimizing the elastic
energy, for elastic ring-shaped objects manipulation. For DOM tasks involving
multiple robots, planning is important for coordination. Alonso-Mora et al.
employed a distributed receding horizon planner for transporting tasks that
require multiple robots [56]. More recently, [57] learns a latent
representation for semantic soft object manipulation that enables (quasi)
shape planning with deformable objects.

With Learning from Demonstration (LfD), the robot can be trained to manipulate
deformable objects by an expert (usually a human). LfD encodes the robot
trajectory and interaction force from human demonstrations [58], thus avoiding
explicitly planning the motion. More recently, Wu et al. have proposed a
reinforcement learning scheme for DOM, which does not require initial
demonstrations [59].

###  V-B Challenges and outlook

A rigid object configuration can be described in space with 6 DoF, whereas a
deformable object configuration has a much higher number of DoF. To address
this from the sensing algorithm side, one can find a compact representation
from sensory data, as discussed in Sect. III-B. An alternative, which receives
much less attention, is the use of environmental contacts to constrain some
DoF of deformable objects. Examples include the use of contact points in cable
harness or that of flat surfaces when folding clothes. We argue that instead
of planning to avoid contacts as most planners do, for deformable objects, we
need to plan to make contact, since this constrains the configuration, and
therefore simplifies the task.

Planning to grasp the correct point is often crucial in DOM tasks. For
instance, grasping at convex vertices of the clothes guarantees stability and
facilitates the task [60]. Re-grasp planning is highly relevant when
considering tasks which require multiple robotic arms. Additional challenges
come from perception, since as soon as the robot releases one or more
grasp(s), the object is likely to change its configuration. We rely on sensing
to track configuration changes and then plan accordingly.

Another important future work in planning is reasoning about a deformable
object at a semantic level. What does it mean for a cloth to be folded? What
does it mean for an object to be wrapped in paper? We cannot manually specify
all the configurations of the deformable object to use as goals in these kinds
of tasks. Instead, we need a way to learn the meaning of semantic concepts,
such as folded or wrapped, so that we can determine if a given configuration
of the object is a valid goal.

##  VI Control

###  VI-A Current capability

Control aims at designing inputs for the robot to realize the planned motion.
The type of controllers is decided usually by the task. For instance, the
authors employed a data-driven model predictive control [61] for cutting
considering its predictive nature and the lower demand for manual tuning. For
safe interaction in minimally invasive surgery, the authors of [62] used a
fuzzy compensator with impedance control. For controlling large deformation,
Aranda et al., proposed a Shape-from-Template algorithm concerning its low
dimensional representation (using the template) and robustness against
occlusion [63].

A number of works focus on shape control. While global models directly map
sensor data to robot motion, local models must be inverted to design the robot
motion controller (see Sec. IV). Several applications of the control scheme
for robotic manipulation of deformable objects can be found in 3C
manufacturing [64, 65], where vision-based controllers were proposed to drive
the robot to automatically grasp/contact the deformable object, then carry out
the task of active deformation or separation/sorting. Other works consider the
concept of diminishing rigidity to do deformation control [66], [67].

###  VI-B Challenges and outlook

Feedback control has been commonly used in most DOM works, by referring to the
state of the object, to achieve the task. Note that such state is retrieved
from the output of its deformation model and measured with sensors, and that
output and state do not necessarily have the same representation and
dimension. Furthermore, we can distinguish between model-based and model-free
control. Due to the complexity of modeling the deformation, when using the
model to derive control policies, the controller has to take into account that
the model will be inaccurate or even wrong.

Model-free approaches do not require information about the deformation
parameters or the structure of the deformation model. Examples include LfD or
(Deep) reinforcement learning, where the challenges are: efficient use of
data, and policy generalization. To address these issues, we can combine the
offline and online learning methods. In the offline phase, the supervised
network can be trained to estimate the model, by collecting pairs of a series
of predefined inputs (e.g., the velocity of the robot end-effector) and the
deformation of the object. The estimated model in the offline phase can be
further updated online during the control task with adaption techniques (e.g.,
the adaptive NNs), to compensate the errors due to insufficient training in
the offline phase or the changes of the deformation model. Hence, both
complement each other.

When multiple features on the deformable object are controlled in parallel,
the system becomes under-actuated, with less control inputs than error
outputs. Then, the robot controller should be able to deal with the conflicts
between multiple features or decouple the control of multiple features in a
sequential manner, to guarantee controllability.

In addition, due to the deformation during control, the contact between robot
end-effector and deformable object may not always be maintained. Most existing
systems require a certain level of human assistance to initiate the contact or
to re-establish it, if it is lost during the task. To improve autonomy, the
robot controller should automatically grasp or touch the object first,
whenever physical contact is lost, laying the foundation of the subsequent
manipulation task. Such a capability would allow the robot to effectively deal
with the unforeseen changes due to deformation.

##  VII Practical applications

In previous sections, we centered our discussions from a scientific point of
view, here, we instead discuss challenges in various applications where DOM
can be translated to solutions.

Automatic laundry: A typical domestic application of DOM is laundry folding. A
Tokyo-based company unveiled its prototype laundry-folding robot in 2015 (Fig.
6a). However, the company was announced bankrupt in 2019 due to lack of
funding for development and difficulties in improving the robot to reach a
satisfactory level [68]. Although cloth folding has been tackled in a few
previous research [69, 70, 71, 72], it remains largely a laboratory product
(limited to structured environments, certain types of the clothes, etc).
Commercializing the technology seems requiring a substantial efforts.

Assistive dressing: Robotic dressing assistance has the potential to become an
important technology due to the pressing needs for ageing society support.
Research can roughly be categorized into simulation-based learning [73, 74]
and imitation learning [75] approaches. Examples are dressing support for
shoes [76], shirts [77, 78, 79] and pants. However, several technical and
societal challenges have to be addressed before robot-assisted dressing will
become a broadly used DOM technology: physical safety for the human, modeling
and prediction of the human-robot interaction, robustness for large variations
of geometric and dynamic properties of textiles, low-cost high-reliable robot
hardware, human acceptance of such technologies.

Surgical robotics: Soft tissue manipulation is mainly performed with tele-
operation solely using visual feedback. Autonomous manipulation, however,
still has a long way to go and demands developing various DOM hardware and
software (Fig. 6d). The biggest concern for an autonomous solution is the
safety of operation. A soft robot with intrinsic compliance will probably
enhance the safety.

Food production & Retail: Handling deformable objects is a major challenge in
the whole chain from production to sales. In an agricultural setting,
automated harvesting of fruits and vegetables requires interactions with
deformable objects that are at the same time easy to damage, which immediately
decreases their value and shelf live. Frequently, these products also undergo
an intermediate processing step (e.g., filleting and packaging meat). More
generally, deformable products (e.g., everything packaged in flexible bags,
(Fig. 6c)) need to be handled in warehouses, in order picking, and in
restocking. Solutions for specific applications and products have been
developed, but more complex objects and operations still are frequently
handled by human workers.

Marine robotics: Underwater grasping has been led by oil and gas industry for
decades, resulting in heavy machines with strong grippers for inspection and
maintenance tasks (Fig. 6e). Gradually the demands turned to more detailed
tasks in marine biology, sedimentology and archaeology (Fig. 6f). Another DOM
application can be found in tethered robot umbilical modeling and control.
Negative buoyancy cable can be modeled in real time as a simple catenary shape
and tracked to control a tethered ROV [80].

Figure 6: Various applications of DOM – (a): laundry-folding robot from Seven
Dreamers Laboratories Inc. [81], (b): A mock-up for robotics dressing
assistance, (c): a robot picking a flexible bag of goods on the shelf,
courtesy AIRLab Delft [82], (d): autonomous surgical manipulation by the dVRK
system [83], (e): ROV Victor 6000 sampling black smokers (IFREMER/GENAVIR)
courtesy D. Desbruyères, (f): Ultra soft underwater gripper for jellyfish [84]

.

##  VIII Summary and key messages

The revolution of robots from automating repetitive tasks to humanizing robot
behaviours is taking place with better hardware, robust sensing capabilities,
accurate modeling, increasingly versatile planning and advanced control.
Manipulation of deformable objects breaks fundamental assumptions in robotics
such as rigidity, known dynamics models and low dimensional state space. It
therefore requires breakthroughs in all the areas mentioned above, and serves
as a great test-bench for novel ideas in both robotic hardware and software. A
summary of challenges and ideas discussed are presented in Fig. 7.

Figure 7: A summary of open research problems and ideas/methods to pursuit
discussed in this paper. Research problems in each subarea are written with
bold black texts, whereas ideas/methods to resolve them are marked with bold
white texts in red eclipses.

In terms of hardware, recently, the community has been shifting more and more
from rigid to soft robots. Robotic manipulation is also gradually shifting
from rigid to deformable objects. One open question is if some of the
algorithms in one field are transferable to the other? We believe the
interaction between a soft robot and a deformable object will bring more
challenges to the robotic community.

Sensing plays a vital part in robotics manipulation of deformable objects.
Depending on the nature and complexity of the task, one or multiple fused
sensing modes may be needed. Machine learning will facilitate the development
of robust algorithms to process data from different sensors, to generate
meaningful representations of deformation.

_All models are wrong, some are useful_. We do not believe there exists the
best model for deformation. While more and more models tend to be data-driven,
we would like to draw the readers’ attention to the importance of physical
models for studying interactions.

For planning, current research lacks a high level semantic reasoning of the
DOM task. Furthermore, while often the purpose of planning is to avoid contact
and collision, we argue that for DOM, it can be very useful to plan for
contact.

Under-actuation is a key challenge of DOM, due to the deformable bodies’ high
DoF. Another practical issue introduced with deformation is contact loss
during manipulation; future controllers should be able to detect contact loss
and to react accordingly.

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PDS 33     I     J     > -7.11     > 0.27     0.168     1.24     0.17$\pm$0.02

PDS 34     I     J     -5.73$_{-0.57}^{+0.54}$     1.75$_{-0.50}^{+0.51}$     0.450     1.24     0.76$\pm$0.07     $\ast$

HD 76534         > Ks     -4.98$_{-0.65}^{+0.66}$     2.43$_{-0.59}^{+0.60}$     0.216     3.35     10.93$\pm$1.44

SAO 220669     I     > Ks     -4.81$_{-0.66}^{+0.66}$     2.42$_{-0.60}^{+0.60}$     0.624     10.15     46.55$\pm$18.57

PDS 286     II     J     -4.26$_{-0.74}^{+0.74}$     3.23$_{-0.70}^{+0.70}$     1.223     1.24     13.77$\pm$1.21

PDS 297          > Ks     -5.77$_{-0.33}^{+0.34}$     1.45$_{-0.31}^{+0.31}$     0.299     11.56     9.76$\pm$3.10

HD 87403          > Ks     -5.20$_{-0.56}^{+0.57}$     1.89$_{-0.52}^{+0.52}$     0.669     22.09     44.70$\pm$5.54

HD 87643     I     J     -4.28$_{-1.15}^{+1.07}$     2.85$_{-0.87}^{+0.77}$     1.168     1.24     6.30$\pm$0.55

PDS 37     I     H     -4.87$_{-0.68}^{+0.67}$     2.48$_{-0.61}^{+0.61}$     0.538     1.66     4.68$\pm$0.47

HD 305298     I     > Ks     -4.64$_{-0.80}^{+0.84}$     3.10$_{-0.73}^{+0.73}$     0.399     3.35     42.05$\pm$5.55

PDS 322          Ks     -4.97$_{-1.01}^{+0.94}$     2.46$_{-0.79}^{+0.72}$     0.114     2.16     6.53$\pm$0.53

HD 94509          > Ks     -5.09$_{-0.57}^{+0.57}$     2.06$_{-0.54}^{+0.54}$     0.982     3.35     5.11$\pm$0.67

PDS 324     I     J     -5.32$_{-0.63}^{+0.62}$     2.15$_{-0.57}^{+0.57}$     0.261     1.24     1.69$\pm$0.15

HD 95881     II     J     -5.06$_{-0.54}^{+0.55}$     1.97$_{-0.52}^{+0.52}$     1.239     1.24     1.12$\pm$0.10

HD 96042     I     > Ks     -4.35$_{-0.74}^{+0.77}$     3.15$_{-0.70}^{+0.70}$     0.994     10.15     199.03$\pm$79.41

HD 97048     I     J     -6.36$_{-0.28}^{+0.28}$     0.99$_{-0.26}^{+0.27}$     0.102     1.24     0.30$\pm$0.03     $\ast$

HD 98922     II     J     -4.96$_{-0.55}^{+0.55}$     2.09$_{-0.53}^{+0.54}$     1.301     1.24     1.40$\pm$0.12

HD 100453     I     J     -7.32$_{-0.21}^{+0.21}$     -0.06$_{-0.18}^{+0.07}$     0.096     1.24     0.09$\pm$0.01     $\ast$

HD 100546     I     J     -6.81$_{-0.25}^{+0.25}$     0.51$_{-0.23}^{+0.23}$     0.097     1.24     0.17$\pm$0.02

HD 101412     II     J     -6.35$_{-0.27}^{+0.27}$     0.87$_{-0.25}^{+0.26}$     0.470     1.24     0.26$\pm$0.02

PDS 344     I     J     -5.97$_{-0.40}^{+0.37}$     1.47$_{-0.33}^{+0.34}$     0.164     1.24     0.52$\pm$0.05     $\ast$

PDS 138     I     > Ks     -3.87$_{-0.89}^{+0.90}$     3.51$_{-0.78}^{+0.78}$     2.395     10.15     387.92$\pm$154.78

HD 104237     II     J     -6.69$_{-0.29}^{+0.29}$     0.46$_{-0.25}^{+0.26}$     0.711     1.24     0.16$\pm$0.01

GSC 8645-1401     I     J     -5.48$_{-0.76}^{+0.52}$     1.49$_{-0.58}^{+0.33}$     1.417     1.24     0.43$\pm$0.04

Hen 2-80     I     J     -4.23$_{-1.57}^{+1.37}$     2.86$_{-1.17}^{+0.82}$     1.310     1.24     6.45$\pm$0.57

Hen 3-823          Ks     -5.15$_{-0.71}^{+0.71}$     2.15$_{-0.60}^{+0.60}$     0.776     2.16     3.49$\pm$0.28

PDS 361S     I     J     -5.26$_{-0.58}^{+0.58}$     2.10$_{-0.54}^{+0.55}$     0.439     1.24     1.52$\pm$0.13

GSC 8994-3902         > Ks     -5.10$_{-0.61}^{+0.60}$     2.19$_{-0.56}^{+0.56}$     0.764     3.35     6.84$\pm$0.90

PDS 364     I     J     -5.15$_{-1.08}^{+1.17}$     1.98$_{-0.80}^{+0.84}$     0.754     1.24     1.15$\pm$0.10

1cMeeus Group
1cJH-K Group
1cLog($\dot{\rm M}_{\rm acc}$)
1cLog(L$_{\rm acc}$)
1cM$_{\rm disk}^{\rm min}$
1cIR$_{\rm start}$
1cr$_{\rm in}$

1c(M$_\odot yr^{-1}$)

Hen 3-938     II     J     -4.08$_{-0.82}^{+0.84}$     3.51$_{-0.75}^{+0.76}$     1.851     1.24     24.04$\pm$2.11

PDS 69     I     H     -5.37$_{-0.71}^{+0.69}$     1.99$_{-0.59}^{+0.58}$     1.028     1.66     1.80$\pm$0.18     $\ast$

DG Cir     I     J     -5.76$_{-0.48}^{+0.46}$     1.32$_{-0.38}^{+0.38}$     0.723     1.24     0.42$\pm$0.04

HD 132947     II     > Ks     -6.33$_{-0.28}^{+0.28}$     0.98$_{-0.26}^{+0.27}$     0.273     10.15     4.87$\pm$1.94     $\ast$

PDS 389     I     H     -5.81$_{-032}^{+0.34}$     1.30$_{-0.30}^{+0.30}$     0.396     1.66     0.61$\pm$0.06

HD 135344B     I     J     -7.28$_{-0.22}^{+0.21}$     -0.14$_{-0.18}^{+0.10}$     0.346     1.24     0.08$\pm$0.01

HD 135344         > Ks     -6.94$_{-0.23}^{+0.22}$     0.19$_{-0.18}^{+0.20}$     0.533     22.09     5.42$\pm$0.67

HD 139614     I     H     -7.29$_{-0.21}^{+0.20}$     -0.02$_{-0.19}^{+0.16}$     0.152     1.66     0.14$\pm$0.01     $\ast$

HD 141569     II     > Ks     -6.77$_{-0.25}^{+0.25}$     0.57$_{-0.23}^{+0.23}$     0.005     3.35     0.69$\pm$0.09

HD 141926     II     J     -4.54$_{-0.72}^{+0.72}$     2.95$_{-0.66}^{+0.66}$     0.621     1.24     8.08$\pm$0.71

HD 142666     II     H     -6.84$_{-0.23}^{+0.23}$     0.29$_{-0.21}^{+0.21}$     0.589     1.66     0.19$\pm$0.02

HD 142527     I     J     -6.54$_{-0.25}^{+0.26}$     0.52$_{-0.23}^{+0.23}$     0.532     1.24     0.17$\pm$0.02

Hen 3-1121     I     J     -4.80$_{-0.86}^{+0.86}$     2.63$_{-0.71}^{+0.71}$     0.519     1.24     4.25$\pm$0.37

Hen 3-1121S          > Ks     -4.58$_{-1.03}^{+0.96}$     3.03$_{-0.81}^{+0.77}$     0.567     10.15     156.97$\pm$62.63

HD 143006     I     J     -7.50$_{-0.22}^{+0.23}$     -0.31$_{-0.17}^{+0.18}$     0.162     1.24     0.07$\pm$0.01

HD 144432     II     J     -6.79$_{-0.24}^{+0.24}$     0.38$_{-0.22}^{+0.22}$     0.611     1.24     0.14$\pm$0.01

HR 5999     II     H     -5.92$_{-0.43}^{+0.44}$     1.16$_{-0.35}^{+0.36}$     0.374     1.66     0.52$\pm$0.05

WRAY 15-1435     I     J     -4.83$_{-0.65}^{+0.67}$     2.51$_{-0.61}^{+0.61}$     0.494     1.24     3.37$\pm$0.30

V718 Sco     II     Ks     -6.93$_{-0.27}^{+0.26}$     0.24$_{-0.23}^{+0.23}$     0.508     2.16     0.26$\pm$0.02

Hen 3-1191     II     J     -5.19$_{-0.71}^{+0.68}$     2.42$_{-0.62}^{+0.63}$     0.674     1.24     2.89$\pm$0.25     $\ast$

HD 149914     II     > Ks     -5.91$_{-0.31}^{+0.30}$     1.24$_{-0.28}^{+0.29}$     0.461     8.23     4.87$\pm$1.62

HD 150193     II     J     -6.78$_{-0.24}^{+0.26}$     0.53$_{-0.23}^{+0.23}$     0.182     1.24     0.18$\pm$0.02     $\ast$

AK Sco     II     H     -7.23$_{-0.43}^{+0.41}$     -0.10$_{-0.29}^{+0.09}$     0.314     1.66     0.12$\pm$0.01

PDS 431     I     > Ks     -6.10$_{-0.32}^{+0.33}$     1.11$_{-0.29}^{+0.30}$     0.536     10.15     5.53$\pm$2.21

V921 Sco     I     J     -4.32$_{-0.82}^{+0.86}$     3.15$_{-0.73}^{+0.73}$     1.065     1.24     11.75$\pm$1.03

HD 155448     I     > Ks     -5.27$_{-0.56}^{+0.56}$     1.88$_{-0.52}^{+0.52}$     0.263     3.35     3.61$\pm$0.48

MWC 878     II     J     -4.54$_{-0.73}^{+0.72}$     3.00$_{-0.68}^{+0.68}$     0.621     1.24     8.99$\pm$0.79

HD 319896     I     Ks     -5.14$_{-0.59}^{+0.59}$     2.13$_{-0.54}^{+0.55}$     0.827     2.16     3.33$\pm$0.27

HD 158643     II     Ks     -5.67$_{-0.32}^{+0.32}$     1.45$_{-0.30}^{+0.30}$     1.017     2.16     1.03$\pm$0.08

HD 323771     II     J     -5.67$_{-0.72}^{+0.67}$     1.71$_{-0.59}^{+0.51}$     0.102     1.24     0.71$\pm$0.06

SAO 185668     I     > Ks     -4.81$_{-0.69}^{+0.67}$     2.45$_{-0.61}^{+0.61}$     0.620     7.95     35.74$\pm$10.10

MWC 593     I?     J     -4.78$_{-0.63}^{+0.62}$     2.41$_{-0.58}^{+0.59}$     0.669     1.24     2.70$\pm$0.24

PDS 469     I     J     -6.39$_{-0.41}^{+0.40}$     0.84$_{-0.34}^{+0.33}$     0.455     1.24     0.25$\pm$0.02

HD 163296     II     J     -6.95$_{-0.31}^{+0.27}$      0.36$_{-0.25}^{+0.25}$      0.145     1.24     0.14$\pm$0.01

PDS 477     I     J     -4.58$_{-1.13}^{+1.04}$     2.70$_{-0.85}^{+0.75}$     0.947     1.24     4.88$\pm$0.43

HD 313571          Ks     -4.76$_{-0.66}^{+0.67}$     2.46$_{-0.60}^{+0.61}$     0.607     2.16     6.40$\pm$0.52

LKHa 260     II     H     -5.60$_{-0.72}^{+0.62}$     1.74$_{-0.58}^{+0.51}$     0.857     1.66     1.10$\pm$0.11

HD 169142     I     J     -7.35$_{-0.20}^{+0.20}$     -0.09$_{-0.18}^{+0.01}$     0.278     1.24     0.09$\pm$0.01

MWC 297     I     J     -4.42$_{-0.69}^{+0.70}$     3.06$_{-0.67}^{+0.67}$     0.846     1.24     9.89$\pm$0.87

VV Ser     II     J     -5.92$_{-0.67}^{+0.55}$     1.51$_{-0.50}^{+0.46}$     0.231     1.24     0.54$\pm$0.05     $\ast$

V431 Sct     II     H     -4.73$_{-0.67}^{+0.66}$     2.65$_{-0.62}^{+0.63}$     0.671     1.66     6.61$\pm$0.67

PDS 520     I     J     -7.06$_{-0.73}^{+0.50}$     0.07$_{-0.38}^{+0.39}$     0.459     1.24     0.10$\pm$0.01

AS 310     I     > Ks     -4.82$_{-0.72}^{+0.71}$     2.79$_{-0.65}^{+0.66}$     0.262     10.15     100.50$\pm$40.10

1cMeeus Group
1cJH-K Group
1cLog($\dot{\rm M}_{\rm acc}$)
1cLog(L$_{\rm acc}$)
1cM$_{\rm disk}^{\rm min}$
1cIR$_{\rm start}$
1cr$_{\rm in}$

1c(M$_\odot yr^{-1}$)

PDS 530     I     H     -7.18$_{-1.07}^{+0.61}$     0.11$_{-0.59}^{+0.46}$     0.275     1.66     0.16$\pm$0.02     $\ast$

MWC 953          J     -4.51$_{-0.82}^{+0.79}$     2.66$_{-0.68}^{+0.67}$     1.135     1.24     4.35$\pm$0.38

PDS 543     I     > Ks     -4.34$_{-0.75}^{+0.78}$     3.24$_{-0.70}^{+0.71}$     1.017     3.35     53.79$\pm$7.09

HD 174571     II     > Ks     -4.49$_{-0.69}^{+0.71}$     2.88$_{-0.66}^{+0.66}$     0.564     7.95     83.57$\pm$23.61

HD 176386          > Ks     -6.49$_{-0.26}^{+0.31}$     0.82$_{-0.25}^{+0.25}$     0.093     3.35     0.92$\pm$0.12

TY CrA     I     J     -6.72$_{-1.09}^{+0.66}$     075$_{-0.65}^{+0.51}$    0.826     1.24     0.23$\pm$0.02     $\ast$

HD 179218     I     H     -5.97$_{-0.29}^{+0.30}$     1.21$_{-0.28}^{+0.28}$     0.201     1.66     0.56$\pm$0.06

HD 344261          > Ks     -7.29$_{-0.21}^{+0.21}$     -0.07$_{-0.18}^{+0.05}$     0.089     22.09     4.08$\pm$0.51     $\ast$

WW Vul     II     J     -6.62$_{-0.32}^{+0.32}$     0.58$_{-0.28}^{+0.28}$     0.622     1.24     0.18$\pm$0.02

PX Vul     II     J     -6.36$_{-0.30}^{+0.32}$     0.66$_{-0.26}^{+0.26}$     0.500     1.24     0.20$\pm$0.02

PDS 581     I     H     -5.06$_{-0.71}^{+0.73}$     2.34$_{-0.62}^{+0.62}$     0.543     1.66     3.59$\pm$0.36

V1295 Aql     II     J     -5.13$_{-0.55}^{+0.56}$     1.92$_{-0.52}^{+0.52}$     1.003     1.24     1.01$\pm$0.09

V1685 Cyg     I     J     -4.95$_{-0.62}^{+0.61}$     2.41$_{-0.58}^{+0.58}$     0.507     1.24     2.77$\pm$0.24

V1686 Cyg     I     J     -6.52$_{-0.92}^{+0.75}$     0.51$_{-0.38}^{+0.46}$     0.495     1.24     0.17$\pm$0.01

MWC 1021     II     Ks     -3.27$_{-0.87}^{+0.87}$     3.66$_{-0.79}^{+0.79}$     9.535     2.16     62.30$\pm$5.04

V1478 Cyg     II     J     -3.69$_{-1.01}^{+0.98}$     3.30$_{-0.80}^{+0.78}$     3.625     1.24     14.96$\pm$1.31

V1977 Cyg     II     J     -5.47$_{-0.49}^{+0.50}$     1.69$_{-0.48}^{+0.48}$     1.171     1.24     0.66$\pm$0.06

V2019 Cyg     I     J     -5.57$_{-0.36}^{+0.37}$     1.63$_{-0.33}^{+0.34}$     1.162     1.24     0.61$\pm$0.05

HBC 705         J     -4.88$_{-0.69}^{+0.67}$     2.50$_{-0.61}^{+0.62}$     0.408     1.24     3.32$\pm$0.29

V1493 Cyg     I     H     -5.25$_{-0.57}^{+0.56}$     1.78$_{-0.51}^{+0.52}$     0.670     1.66     1.14$\pm$0.12

HBC 717     I     J     -6.50$_{-0.38}^{+0.38}$     0.53$_{-0.29}^{+0.30}$     0.496     1.24     0.17$\pm$0.02

HD 199603     II     > Ks     -6.55$_{-0.25}^{+0.26}$     0.56$_{-0.23}^{+0.23}$     0.685     21.73     8.09$\pm$2.49

HD 200775     I     H     -5.03$_{-0.58}^{+0.58}$     2.24$_{-0.55}^{+0.55}$     1.026     1.66     2.94$\pm$0.30

LkHa 324          > Ks     -6.04$_{-0.36}^{+0.33}$     1.30$_{-0.31}^{+0.31}$     0.276     3.35     1.61$\pm$0.21

HD 235495     II     J     -6.08$_{-0.30}^{+0.31}$     1.12$_{-0.28}^{+0.29}$     0.389     1.24     0.34$\pm$0.03

AS 470         Ks     -4.26$_{-0.78}^{+0.79}$     2.49$_{-0.67}^{+0.66}$     1.582     2.16     6.22$\pm$0.50

GSC 3975-0579     I?     J     -6.41$_{-0.27}^{+0.27}$     0.80$_{-0.26}^{+0.25}$     0.345     1.24     0.24$\pm$0.02

V361 Cep          Ks     -5.30$_{-0.56}^{+0.56}$     2.04$_{-0.52}^{+0.52}$     0.108     2.16     2.85$\pm$0.23

V373 Cep          J     -5.67$_{-0.34}^{+0.34}$     1.62$_{-0.32}^{+0.33}$     0.903     1.24     0.61$\pm$0.05

AS 477     II     J     -5.61$_{-0.63}^{+0.57}$     1.55$_{-0.50}^{+0.43}$     1.122     1.24     0.55$\pm$0.05

LkHa 257     I     J     -6.92$_{-0.24}^{+0.23}$     0.40$_{-0.22}^{+0.22}$     0.086     1.24     0.15$\pm$0.01

BH Cep     II     J     -7.21$_{-0.32}^{+0.32}$     -0.05$_{-0.25}^{+0.16}$     0.259     1.24     0.09$\pm$0.01

BO Cep     I     H     -7.40$_{-0.20}^{+0.19}$     -0.22$_{-0.17}^{+0.17}$     0.255     1.66     0.11$\pm$0.01

SV Cep     II     H     -6.74$_{-0.34}^{+0.33}$     0.49$_{-0.28}^{+0.28}$     0.503     1.66     0.25$\pm$0.03

MWC 655     I     J     -4.70$_{-0.67}^{+0.67}$     2.61$_{-0.62}^{+0.62}$     0.652     1.24     4.12$\pm$0.36

IL Cep     II     > Ks     -4.80$_{-0.62}^{+0.62}$     2.56$_{-0.59}^{+0.59}$     0.575     4.60     21.52$\pm$3.25

V374 Cep     I     J     -5.05$_{-1.15}^{+1.02}$     2.23$_{-0.84}^{+0.71}$     0.940     1.24     1.94$\pm$0.17

MWC 1080     I     J     -4.57$_{-0.86}^{+0.85}$     2.99$_{-0.72}^{+0.72}$     0.580     1.24     8.66$\pm$0.76

BP Psc     I     J     -7.65$_{-0.59}^{+0.56}$     -0.46$_{-0.41}^{+0.33}$     0.125     1.24     0.06$\pm$0.01

LkHa 259     I     J     -6.32$_{-0.28}^{+0.27}$     0.76$_{-0.25}^{+0.25}$     0.610     1.24     0.22$\pm$0.02

For the stars with $\text{an asterisk}$ in the last column, accretion-based disk masses have been reestimated because t$_{*}$ > t$_{\rm MS}$ (Sect. <ref>).

Disk masses derived by millimeter fluxes

1cT$_{\rm D}$
1cM$_{\rm disk}$
1cNº photometric points

HBC 1     1.0     21     7.808$\pm$0.887     1     (16)

VX Cas     1.0     33     < 0.007     1     (28)

V594 Cas     1.1     32     0.039$\pm$0.001     2     (7) (32)

HD 9672     0.6     39     2.920E-4$\pm$3.060E-5     2     (25)

AB Aur     1.2     40     0.009$\pm$0.002     5     (1) (2) (3)

HD 31648     0.9     20     0.051$\pm$4.410E-4     6     (1) (2) (5) (20)

UX Ori     0.8     22     0.016$\pm$0.001     2     (28) (33)

HD 34282     1.5     38     0.040$\pm$0.004     6     (1) (11) (16) (21)

HD 34700     1.1     28     0.008$\pm$0.001     4     (8) (11) (22) (23)

HD 35187     0.5     42     0.003$\pm$1.800E-4     3     (1) (4)

CO Ori     1.0     16     < 0.006     1     (8)

HD 36112     1.5     31     0.006$\pm$1.140E-4     3     (1) (5)

HD 245185     0.1     46     0.016$\pm$0.003     2     (5)

T Ori     1.0     28     0.108$\pm$0.023     1     (8)

CQ Tau     0.4     19     0.028$\pm$3.410E-4     2     (5)

V380 Ori     1.0     33     0.041$\pm$0.016     1     (35)

BF Ori     1.0     25     0.005$\pm$0.002     1     (8)

HD 290764     1.0     19     0.244$\pm$0.026     1     (19)

V599 Ori     1.0     22     0.091$\pm$0.007     1     (37)

RR Tau     0.3     29     0.058$\pm$0.005     2     (32)

HD 250550     1.0     38     < 0.085     1     (7)

HD 41511     0.3     16     0.019$\pm$0.002     2     (2)

GSC 1876-0892     1.0     71     19.646$\pm$6.445     1     (9)

LkHa 208     1.0     17     < 0.014     1     (28)

MWC 137     1.2     143     1.948$\pm$0.281     6     (14)

VY Mon     1.9     58     0.052$\pm$0.006     5     (1) (32)

LkHa 215     1.8     70     0.061$\pm$0.015     3     (14)

HD 259431     1.0     44     < 0.052     1     (14)

HT CMa     1.0     33     < 0.180     1     (6)

Z CMa     1.9     36     1.383$\pm$0.017     8     (34)

PDS 241     1.0     172     57.362$\pm$1.616     9     (29)

V388 Vel     1.9     47     0.294$\pm$0.093     3     (36)

HD 76534     1.0     101     < 0.019     1     (6)

PDS 37     1.0     101     15.663$\pm$3.040     1     (30)

HD 97048     1.6     24     0.094$\pm$0.007     3     (26) (27)

HD 100453     1.0     17     0.025$\pm$0.002     1     (4)

HD 100546     1.3     13     0.061$\pm$0.003     4     (4) (6) (10)

HD 104237     1.0     19     0.008$\pm$0.002     1     (6)

HD 135344B     1.4     30     0.013$\pm$0.002     3     (1) (11)

HD 135344     1.7     27     0.011$\pm$0.009     3     (10)

HD 139614     0.6     29     0.022$\pm$0.001     4     (4) (11)

HD 141569     1.0     46     1.460E-4$\pm$1.570E-5     3     (1) (5)

HD 142666     0.5     30     0.013$\pm$0.001     3     (1) (11)

HD 142527     0.3     19     0.211$\pm$5.810E-5     2     (5)

HD 143006     1.0     15     0.032$\pm$4.940E-5     1     (12)

HD 144432     1.6     6     0.021$\pm$0.002     3     (4)

HR 5999     0.0     15     0.008$\pm$2.190E-4     2     (1) (13)

HD 150193     0.6     40     0.004$\pm$0.001     4     (1) (2) (4)

AK Sco     0.3     27     0.003$\pm$7.350E-6     4     (4) (5)

V921 Sco     1.0     215     0.360$\pm$0.047     1     (7)

HD 158643     1.0     28     3.780E-4$\pm$4.530E-5     1     (13)

HD 163296     0.4     34     0.034$\pm$0.001     8     (14)

HD 169142     1.2     31     0.010$\pm$3.090E-4     5     (1) (4) (5)

MWC 297     0.0     200     0.029$\pm$0.001     3     (1) (6)

VV Ser     0.0     35     9.540E-4$\pm$2.730E-4     2     (32)

V431 Sct     1.0     101     0.225$\pm$0.062     1     (6)

1cT$_{\rm D}$
1cM$_{\rm disk}$
1cNº photometric points

PDS 520     1.0     16     0.162$\pm$0.021     1     (31)

AS 310     1.0     215     0.768$\pm$0.050     1     (6)

HD 176386     1.0     33     0.121$\pm$0.010     1     (15)

TY CrA     1.0     38     < 0.017     1     (17)

HD 179218     1.4     24     0.029$\pm$0.003     2     (16)

WW Vul     1.0     23     0.016$\pm$0.001     1     (4)

V1685 Cyg     1.0     101     0.255$\pm$0.033     1     (7)

V1686 Cyg     1.0     16     < 0.040     1     (8)

V1478 Cyg     0.0     35     12.973$\pm$0.349     2     (1)

HD 200775     1.0     71     < 0.015     1     (17)

HD 235495     1.0     33     0.038$\pm$0.005     1     (18)

V361 Cep     1.0     71     < 0.032     1     (7)

V373 Cep     1.0     44     < 0.051     1     (34)

AS 477     1.0     33     < 0.051     1     (7)

SV Cep     1.0     23     0.005$\pm$0.001     1     (28)

MWC 1080     1.6     229     0.308$\pm$0.039     7     (14)

LkHa 259     1.0     18     93.196$\pm$40.276     1     (10)

mm flux measurements: (1) <cit.>; (2) <cit.>; (3) <cit.>; (4) <cit.>; (5) <cit.>; (6) <cit.>; (7) <cit.>; (8) <cit.>; (9) <cit.>; (10) <cit.>; (11) <cit.>; (12) <cit.>; (13) <cit.>; (14) <cit.>; (15) <cit.>; (16) <cit.>; (17) <cit.>; (18) <cit.>; (19) <cit.>; (20) <cit.>; (21) <cit.>;
(22) <cit.>; (23) <cit.>; (24) <cit.>; (25) <cit.>; (26) <cit.>; (27) <cit.>; (28) <cit.>; (29) <cit.>; (30) <cit.>; (31) <cit.>; (32) <cit.>; (33) <cit.>; (34) <cit.>; (35) <cit.>; (36) <cit.>; (37) <cit.>;

§ SEDS

SEDs of the whole sample. The  solid blue line corresponds to the best photospheric model that fits the deredenned optical photometry (red dots). Yellow triangles are upper limits.