[1]Shubhan P. Patni These authors contributed equally to this work.

These authors contributed equally to this work.

[1]Department of Cybernetics, Faculty of Electrical Engineering, Czech
Technical University in Prague

2]Department of Mechanics, Biomechanics and Mechatronics, Faculty of
Mechanical Engineering, Czech Technical University in Prague

# Evaluating online elasticity estimation of soft objects using standard robot
grippers

<EMAIL_ADDRESS>Pavel Stoudek  Hynek Chlup  Matej Hoffmann  *  [

###### Abstract

Stiffness or elasticity estimation of everyday objects using robot grippers is
highly desired for object recognition or classification in application areas
like food handling and single-stream object sorting. However, standard robot
grippers are not designed for elasticity estimation. In this work, a
professional biaxial compression device was used as a control setup to study
the accuracy with which material properties can be estimated by two standard
parallel jaw grippers and a force/torque sensor mounted at the robot wrist.
Using three sets of deformable objects, different parameters were varied to
observe their effect on measuring material characteristics: (1) repeated
compression cycles, (2) compression speed, and (3) the surface area of the
gripper jaws. Gripper effort versus position curves were obtained and
transformed into stress/strain curves. The modulus of elasticity was estimated
at different strain points. Viscoelasticity was assessed using the energy
absorbed in a compression/decompression cycle, the Kelvin-Voigt, and Hunt-
Crossley models. Our results can be summarized as follows: (1) better results
were obtained with slower compression speeds, while additional compression
cycles or surface area did not improve estimation; (2) the robot grippers,
even after calibration, were found to have a limited capability of delivering
accurate estimates of absolute values of Young’s modulus and viscoelasticity;
(3) relative ordering of material characteristics was largely consistent
across different grippers; (4) despite the nonlinear characteristics of
deformable objects, fitting linear stress/strain approximations led to more
stable results than local estimates of Young’s modulus; (5) to assess
viscoelasticity, the Hunt-Crossley model worked best. Finally, we show that a
two-dimensional space representing elasticity and viscoelasticity estimates is
advantageous for the discrimination of deformable objects. A single-grasp,
online, classification and sorting of such objects is thus possible. An
additional contribution is the dataset and data processing codes that we make
publicly available.

###### keywords:

Material property estimation; Deformable objects; Haptic object exploration

##  1 Introduction

Although visual object recognition has seen tremendous progress in recent
years, not all object properties can be perceived using distal sensing. In
particular, physical object properties like stiffness, roughness, or mass are
better perceived through manipulation. Object recognition from haptic
exploration can be more robust as it is insensitive to lighting conditions and
object attributes that may be irrelevant (e.g. color). Estimating and
interpreting these properties are desirable in many application areas such as
single-stream object picking for manufacture [1, 2] or recycling. Plastic,
paper, and metal differ significantly in their material properties and sorting
them through manipulation holds great promise [3]. Further, in application
areas such as virtual/augmented reality [4], medical diagnosis through
palpation of subcutaneous tissue [5], and during tele-operation for navigating
unknown environments, deformable objects need to be perceived and handled.

Sanchez et al. [6] provide a survey of robotic manipulation and sensing of
deformable objects. Objects are considered deformable if they have no
compression strength (ropes and clothes) or have a large strain111For linear
elasticity, this implies small Young’s modulus, e.g. less than 10000 kPa..
Additionally, classification based on geometry is presented. In this work, we
leave objects of Type I-III (linear, planar, cloth-like) aside and focus on
Type IV: triparametric objects—solid objects such as sponges or plush toys,
which are also the least researched object type [6]. Computational costs when
simulating these interactions are enormous.

In this work, we specifically focus on material elasticity and
viscoelasticity, and to what extent it can be estimated online using common
robot equipment like 2-finger grippers. Grippers are designed for grasping
rather than stiffness estimation, and often lack tactile sensors at the
fingertips, hence their ability to provide accurate estimates of physical
quantities like the modulus of elasticity is limited. With the help of a
professional biaxial compression testing device, we systematically assess the
performance of these grippers and a force sensor at the robot wrist, under
different settings.

This article is structured as follows. After reviewing related work, the
essentials of physics of deformation are explained (Section 3). Sample objects
and the measuring devices are described in Section 4, followed by Experiments
and Results. We close with Conclusion, Discussion, and Future work.

The dataset including raw as well as processed data collected during the
experiments in this work is publicly available [7, 8]. An accompanying video
is available here: https://youtu.be/FCNV24ZcOnM.

##  2 Related work

Recent surveys of haptic or tactile robot perception are provided by [9, 10].
Li et al. [9] list the object and material properties that can be extracted
via tactile perception: stiffness, friction, surface texture, thermal
conductivity, and adhesion. However, Luo et al. [10] point out a gap between
rapid development of tactile sensing hardware and insufficient knowledge about
how to interpret the sensory information obtained. In this paper, we try to
reduce this gap by exploring the data streamed from the sensors and extracting
material properties that may improve the interactions between robots and
objects. We focus on stiffness/elasticity and how it can be perceived through
a pinch grasp (squeezing). For deformable objects, the same action also allows
us to perceive another material property: viscoelasticity. The next
subsections provide an overview of the latest research in estimating stiffness
and viscoelasticity in a robotic setup, i.e. without the use of industrial
precision measurement instruments but rather with sensors commonly integrated
with robots—RGB-D cameras and tactile sensors that measure reaction force.

###  2.1 Object Discrimination from Tactile Feedback

Spiers et al. [11] used a two-finger compliant gripper with force sensors to
classify objects of various shapes, sizes, and stiffness. Random forests were
used for classification and the importance of different extracted features was
evaluated. Delgado et al. [12] used the Shadow Hand to grasp deformable
objects and computed the deformability ratio to infer the maximum force
allowed to be exerted on the object. Hosoda and Iwase [13] used a human-like
robot hand with artificial muscles and soft skin with tactile receptors as
input to a recurrent neural network with context nodes for object
classification. Industrial research in the area is focused towards recognising
objects for improved grasping and manipulation. Gemici and Saxena [14] learned
haptic representations of food items. Four actions were used to explore 6
object characteristics (hardness, plasticity, elasticity, tensile strength,
adhesiveness, brittleness). Scimeca et al. [15] used a 2-finger gripper for
mango ripeness estimation. Chin et al. [3] implemented a custom-made soft
2-finger gripper with pressure and strain sensors to automated recycling
separation (paper, plastic, metal). Finally, most related to this work, Wang
et al. [16] used the deformation cues from pinch grasps of different soft
objects to classify them using Functional Principal Component Analysis (FPCA
features).

###  2.2 Estimating Elasticity

Smardzewski et al. [17] employ a professional axial compression device for
estimating the compressive modulus of elasticity, in line with the
corresponding standards [18]. Such measurement is very different from
practical robotics because of the speed of testing, the precision of the
feedback, and the varying shapes and sizes of objects. Some works employ the
Finite Element Method (FEM) to model the object based on deformation data.
Frank et al. [19] estimated the stiffness by capturing the object via RGB-D
camera, creating a three dimensional finite element mesh in simulation
software, and then numerically optimizing the stiffness parameter of the mesh
by minimizing the error between the simulated and observed deformations. This
process was developed upon further in [20] which used the simulated model and
obtained stiffness to compute the input force for any given deformation.
Visual and haptic information was also combined in [21] to estimate mechanical
parameters of soft tissue. Longhini et al. [22] used visual tracking of marker
nodes placed on the surface of the deforming object to learn deformation
models of various textiles for control and manipulation. Stress-strain models
were used to gain information about deformable materials without explicitly
extracting stiffness/elasticity values in [23]. Narang et al. [24] used
feedback from the BioTac tactile sensor as input to a multi-layer perceptron
network predict the deformation of the target object in simulation. The
network was trained to convert feedback to deformation and vice versa via a
latent space representation. This solution was applied to a medical scenario
in [25] for estimating the variable stiffness of soft tissue. However, the
finite element method comprises of optimizing the target parameter for a large
number of nodes. It is computationally time consuming and cannot be employed
for quick, online estimation. Further, these articles use the ‘poking’ action
by pressing the object against a wall with a fingertip, while in this work, we
employ ‘squeezing’ or pinching between the gripper jaws. Zaidi et al. [26]
employed a fingertip contact model that also simulates the deformation of the
target object. The stiffness and damping are computed at the contact point and
used as parameters in the deformation simulation to estimate grasp stability.
Haddadi et al. [27] used the Hunt-Crossley Dynamic model for real-time
identification of contact environments. This method is quicker as compared to
finite element methods because it regards the object as a whole rather than as
a mesh of a large number of nodes. Only three parameters have to be computed
from collected force vs. deformation data. Further, no visual mode is applied,
the feedback is only from the gripper and attached force sensors. Bednarek et
al. [28] did not use a robotic hand or gripper, but instead use a spherical
tip with the OptoForce 3-axis optical force sensor. The time series from this
sensor is processed using an LSTM employed for material classification. Yao et
al. [29] used the compression action to create three-dimensional stiffness
maps of household objects.

###  2.3 Our Contribution

The focus of this work is to investigate how much can be learned about objects
from a few grasping/squeezing actions. The contributions of this work over the
state of the art are the following.

  1. 1.

We use three different robotic devices (two parallel jaw grippers and one
force/torque sensor at the robot flange) and systematically study the effect
of the characteristics of the device itself and different parameters of the
object compression process on the quality of the mechanical response curves.

  2. 2.

We test a large set of deformable objects and employ a professional biaxial
compression device to provide control values.

  3. 3.

We assess the potential and limitations of robot grippers to gauge material
elasticity—absolute values of Young modulus as well as relative ordering of
objects by their elasticity.

  4. 4.

We study the viscolelastic properties of the objects through compression and
decompression cycles at different speeds.

  5. 5.

The collected dataset including the code for data processing is made publicly
available.

Finally, we draw conclusions that generalize beyond the specific devices used
here and provide guidelines for practical elasticity estimation and deformable
object discrimination using ordinary robot grippers.

##  3 Physics of deformation

###  3.1 Elasticity

If a force is exerted on an object, the object deforms and it’s dimensions
change.222This section draws on [30, Ch. 9] Depending on the direction of the
force, the object either compresses or elongates. In this work, we focus on
axial compression as this mode of testing objects/materials applies to robot
grippers. If the amount of compression, $\Delta L$, is small compared to the
length of the object, $\Delta L$ is proportional to the force exerted. This is
sometimes referred to as Hooke’s law and can be written as

$F=k\Delta L,$ (1)

where F represents the force applied on the object, $\Delta L$ is the change
in length, and k is a proportionality constant. This linear relationship is a
good approximation for many common materials, but applies only up to a certain
$\Delta L$ called the proportional limit. With additional compression, the
linear relationship does not hold anymore, but up to the elastic limit, if the
force is released, the object still fully returns to its original dimensions.
The strain is the ratio of the change in length $\Delta L$ to the original
length $L_{0}$. It is proportional to the force applied and the original
length, but also inversely proportional to the cross-sectional area. To
eliminate the object’s size or shape, a constant of proportionality that
depends only on the object material is desired. This is the elastic modulus or
Young’s modulus, E:

$E=\frac{stress}{strain}=\frac{F/A}{\Delta L/L_{0}},$ (2)

where stress is the force (F) per unit area (A) and has thus units $Nm^{-2}$,
or Pascals. For the soft materials in this work, we will use kiloPascals
(kPa). Strain is a dimensionless quantity (no units).

###  3.2 Viscoelasticity

Soft objects like the polyurethane foams, for example, have an elastic
component and a viscoelastic component. Due to molecular rearrangement, energy
as heat is dissipated when a load is is applied and then removed, i.e. during
a compression and decompression cycle. The strain rate is also time-dependent.
These properties can be characterized by the hysteresis in the stress-strain
curve or by models taking into account both elasticity and viscosity. These
will be detailed below.

####  3.2.1 Calculating Viscoelasticity from Loop Enclosed Area

The “paths” for compression and decompression on the stress/strain plot are
different for deformable objects. There is an area enclosed by these paths—the
hysteresis loop—which corresponds to the amount of energy lost (as heat) as
shown in Fig. 1. By plotting the energy lost versus the speed of
compression/release we can obtain the viscoelastic coefficient $\eta$.

Figure 1: Sample Hysteresis Curve

####  3.2.2 Kelvin-Voigt Model

The Kelvin-Voigt model is a simple model that views every object as a spring
and damper system arranged in parallel. The equation used to describe objects
is a linear second order differential equation:

$F(x(t),\dot{x}(t))=Kx(t)+\eta\dot{x}(t)$ (3)

where $F$ is the applied force, $K$ is the stiffness/elasticity parameter,
$\eta$ is the damping/hysteresis parameter, $x$(t) and $\dot{x}$(t) are the
deformation and rate of deformation respectively. Once a cycle of compression
and release data has been collected in the form of deformation and force
feedback, this data can be fit into Eqn. (3) using multi-variable linear
regression to obtain values of $K$ and $\eta$.

####  3.2.3 Hunt-Crossley Model

The Hunt-Crossley model expands upon the simple Kelvin-Voigt model by adding
nonlinear power terms to the stiffness and damping components. Eqn. (3) is
modified as

$F(x(t),\dot{x}(t))=Kx^{n}(t)+\eta x^{n}(t)\dot{x}(t)$ (4)

The added power terms $x^{n}(t)$ accommodate the nonlinearities of the
material. The term $n$ is a new parameter obtained as a result of the model.
Since it is an exponential, instead of fitting data on this equation, we fit
data on the logarithmic form:

$\log(F(x,\dot{x}))=\log(K)+n\log(x)+\log[1+\frac{\eta\dot{x}}{K}]$ (5)

##  4 Experimental setup

The set of object samples is described, followed by the robot grippers and a
professional measuring device. Additional details about the experimental
procedure and how the robot grippers were commanded can be found in a student
thesis [31]. The code used to command the grippers and preprocess data is
available at [32].

###  4.1 Objects set

We considered two sets of deformable objects. The first set, cubes and dice,
consisted of 7 cuboid objects with a different size and degree of softness.
The second set, polyurethane foams set, consisted of 20 polyurethane foam
blocks of similar size, along with reference values for elasticity and density
provided by the manufacturer. For all the objects used, the deformation can be
regarded as elastic—objects returned to their undeformed shapes once the
external force is removed. For some objects, this recovery was slow and they
can be regarded as viscoelastic.

##### Cubes and dice set

This set of 7 soft objects is visualized in Fig.2(a) together with their
names. Their dimensions are listed in Table 1. The “blue cube” is composed of
the same material like the “blue die”—it has been cut out from another
exemplar of the same object. “White die”, “kinova cube”, yellow cube”, and
“blue cube” have roughly same dimensions but different material composition.
The dataset was deliberately designed in this way such that the effects of
material elasticity and object shape and size would be apparent in the
results.

Figure 2: (a) Cubes and Dice set; (b) Polyurethane foams set; (c) Mixed set Table 1: Cubes and dice – dimensions. Description | Dimensions [mm]
---|---
Kinova cube | 56x56x56
Blue cube | 56x56x56
Yellow cube | 56x56x56
Blue die | 90x90x90
White die | 59x59x59
Pink die | 75x75x75
Darkblue die | 43x43x43

##### Polyurethane foams set

To complement the “ordinary objects set”, we tested on another set of objects:
20 polyurethane foams (Fig.2(b)). These were samples provided by a
manufacturer of mattresses and other foam products. The set includes hard
insulation foams, memory foams, mattress foams and soundproof foams. Compared
to the ordinary soft objects, “cubes and dice”, this dataset is much more
uniform—both in terms of object dimensions and elasticity. The first two
letters code for the standardized material type. For example, “RP” stands for
Richfoam Polyether (STANDARD 100 by OEKO-TEX); the “T” series are polyurethane
foams used to make furniture (hyper elastic polyurethane furniture foams
[17]). Additionally, the complete code also contains density and one measure
of the material’s elasticity: the compression stress value at 40% compression
($CV_{40}$ [18]) – see Table 2. However, we could not directly use these
elasticity values as reference because the testing conditions prescribed by
the ISO standard [18] cannot be met with robot grippers; moreover, these
values have been obtained from samples tested within 72 hours after
manufacture.

Table 2: Polyurethane foams set. Label – code supplied by manufacturer. Density is expressed in ${kg\cdot m^{-3}}$. Elasticity is the $CV_{40}$ in kPa – compression stress value at 40% strain [18]. Label | Dimensions [mm] | Density | $CV_{40}$
---|---|---|---
V4515 | 118x120x40 | 45 | 1.5
V5015 | 119x120x42 | 50 | 1.5
GV5030 | 118x119x40 | 50 | 3.0
GV5040 | 118x118x39 | 50 | 4.0
N4072 | 118x117x37 | 40 | 7.2
NF2140 | 105x100x50 | 21 | 4.0
T1820 | 125x125x50 | 18 | 2.0
T2030 | 125x120x40 | 20 | 3.0
T3240 | 123x123x50 | 32 | 4.0
T2545 | 125x125x50 | 25 | 4.5
RL3529 | 119x118x40 | 35 | 2.9
RL4040 | 117x120x40 | 40 | 4.0
RL5045 | 118x118x39 | 50 | 4.5
RP1725 | 118x120x41 | 17 | 2.5
RP2440 | 118x120x38 | 24 | 4.0
RP27045 | 117x119x39 | 270 | 4.5
RP30048 | 123x121x39 | 300 | 4.8
RP3555 | 117x119x39 | 35 | 5.5
RP2865 | 118x118x38 | 28 | 6.5
RP50080 | 121x118x39 | 500 | 8.0
|  |  |

##### Mixed set

Due to the reasons cited above, we need to obtain reference or control values
for elasticity that the materials show in real time rather than their
properties at manufacture time. An additional object set was formed from the
previous sets, taking two “cubes and dice” (“Blue die” and “Kinova cube”) and
6 polyurethane foams – Fig.2(c). This set of 8 objects was tested on a
professional biaxial compression setup (Section 4.4) to provide a reference
for the measurements using robot grippers.

###  4.2 Robot setups

For experimentation, the following robotic setups are used: the Universal
Robot UR10 with the OnRobot RG6 gripper and the Kinova Gen3 robotic arm with
the Robotiq 2F-85 gripper. In addition, a force/torque sensor Robotiq FT300
was appended to the UR10 robot as a makeshift third setup.

####  4.2.1 Robotiq 2F-85

This gripper (Fig.3(a)) has 2 fingers with 85 mm stroke and offers a grip
force from 20 N to 235 N. The fingertips dimensions can be approximated to a
rectangle of $37.5\times 22\,\mathrm{mm}$. Velocity control was used during
object compression. This is quoted in % of the maximum closing speed.

Figure 3: (a) Robotiq 2F-85; (b) OnRobot RG6; (c) Robotiq FT300

Action parameters: Four different nominal squeezing speeds were executed:
0.68% (approx. 1.6 mm/s), 14.45% (30 mm/s), 50.85% (80 mm/s), and 100% (131.33
mm/s).

Sensory channels: 2 channels: gripper position (gap between jaws 0–85 mm),
motor current (A).

####  4.2.2 OnRobot RG6

The gripper (Fig.3(b)) has a 160 mm stroke and adjustable force and gripper
status feedback (digital and analog). Gripper fingertips’ surface area is
$866\,\mathrm{mm}^{2}$. Continuous closing while recording force feedback is
not possible—it can only be emulated by incrementally increasing the force
threshold.

Action parameters: None. The gripper was commanded to close with 1 mm
increments until a certain force threshold was reached. Then, the threshold
was incrementally increased. The force range was 25-120 N, with 1 N
increments.

Sensory channels: 2 channels: gripper position (gap between jaws 0–160 mm) and
flag for force threshold reached, plus the actual threshold (N). Data was
collected only at the occasions when force threshold was reached.

####  4.2.3 Robotiq FT300

The UR10e manipulator is equipped with a Robotiq FT300 force/torque sensor
(Fig.3(c)) that has a measuring range $\pm 300\,\mathrm{N}$ and $\pm
30\,\mathrm{N}\cdot\mathrm{m}$ for every axis in Cartesian coordinate system.
The sensor noise for the force measurements should be 0.033 %.

Action parameters: None. We pressed the objects with the robot flange against
the table with a speed of 30 mm/s.

Sensory channels: 2 channels: position in z-axis (mm) and force in the
downward direction (N).

###  4.3 Gripper calibration

We used a S9M/500 N force transducer (strain gauge) along with a ClipX
amplifier system (both from HBM) to calibrate the force feedback from the
robotic grippers.

The Robotiq 2F-85 gripper outputs motor current in the range 0-1 A.
Measurements were collected by manually operating the gripper as well as using
velocity control with the range of speeds used later in the experiments. The
relationship of force and current was found to be nonlinear and the best fit
obtained was:

$F_{2F-85}=87.6i^{3}-216.0i^{2}+191.4i+0.18$ (6)

where i was the current reading (in Amperes) obtained from the gripper.
Additionally, the closing speeds in % had to be calibrated and converted to
mm/s (using the gripper position signal).

For the OnRobot RG6 gripper, feedback in Newtons is available. However, we
have performed calibration as well and an approximately linear fit was
obtained.

$F_{Actual}=0.8678\times F_{RG6}-2.13$ (7)

###  4.4 Professional biaxial compression setup

This setup was deployed to provide reference or control measurements for the
“mixed set” of objects (Section 4.1). A biaxial experimental system
Zwick/Roell was used (see Fig. 4). Samples were cyclically compressed between
two antagonistic actuators, with a position resolution of $1\mu\cdot m$. The
actuator axes were connected to force sensors U9B from HBM with a 0.5 kN
range, set to $\pm 250$ N, suitable for static and dynamic force measurements
(accuracy class 0.2; IP67). On every side, a transparent pad of plexiglass was
attached, with dimensions $59\times 59\times 10$ mm and mass of 60 g. The
sample was placed between the pads and cyclically compressed and decompressed
from both sides. Six cycles of compression and decompression were performed
for every sample.

Action parameters: Compression speeds: One sample (RP1725) was tested with 1,
1.6, 10 30, 50, 80 mm/s. Remaining samples from the mixed set were tested with
1.6, 30, 50, and 80 mm/s. Decompression speed was the same as compression
speed with the exception of sample V4515 which took long to restore its
volume—1.6 mm/s decompression was used.

Sensory channels: Force (N) and displacement (mm) at every actuator.

Figure 4: Professional setup for elasticity measurements.

##  5 Experiments and results

The presentation of experiments starts with plots of mechanical response
curves from the different devices in their standard units, followed by a
transformation into stress/strain curves. The effect of compression speed and
precycling is analyzed. Young modulus estimates are then compared. Finally,
viscoelastic property of the objects is studied.

Illustration of some of the experiments is available in the accompanying
video.

###  5.1 Gripper effort and position

We compare the raw plots that can be obtained in the standard operation mode
of every robotic device, as shown in Fig. 5 for the cubes and dice. No
preprocessing or filtering of the data is applied. On the x-axes, object
compression proceeds from right to left, as the gripper width decreases.
Contact with the object is not detected and as the objects have different
width, the curves corresponding to gripper effort start rising at different
locations.

For the Robotiq 2F-85 gripper, 50% compression speed (approx. 79 mm/s) was
used. Motor current is plotted against the gripper width. For the OnRobot RG6
gripper, force feedback can be retrieved only during discontinuous object
compression with incremental adjustment of the force threshold. During
measurements with the FT300 sensor, the robot arm was commanded to press
downward against the object with a speed of 30 mm/s.

From Fig. 5, it is apparent that the mechanical response curves from all three
devices have similar characteristics. The force/torque sensor (Fig.5(c),(f))
delivers the most clean data. The lines on the OnRobot RG6 plot (Fig.5(b),(e))
are noisy and not monotonic. This is because they were not collected during
continuous compression of the objects, but through incremental increasing of
the force threshold. The least accurate response curves come from the Robotiq
2F-85 (Fig.5(a),(d)), mainly because there are too few data points
(combination of limited sampling rate and high speed of compression).

Figure 5: (a)-(c) Cubes and dice set–gripper feedback vs gripper position.(a)
Robotiq 2F-85; (b) OnRobot RG6; (c) Robotiq FT300. (d)-(f) Polyurethane foams
set–gripper feedback vs gripper position. (d) Robotiq 2F-85; (e) OnRobot RG6;
(f) Robotiq FT300.

The 20 polyurethane foams constitute a more homogeneous object set, with
similar dimensions and a narrower range of elasticity. Similar observations
about the precision and continuity of data can be made for the deformable
objects set and the polyurethane foams set.

###  5.2 Stress/strain response curves

To estimate material elasticity, the stress/strain relationship during
compression of the material in question needs to be obtained (see Section 3
and Eqn. (2)). The key requirement is to detect the moment of contact of the
gripper with the object, which marks the beginning of the stress/strain curve;
the gripper width corresponds to $L_{0}$. To recognize the moment of contact,
the force/effort needs to be measured, which is necessary at any rate to
obtain stress. The accuracy of contact detection affects the results and is
gripper dependent. Position can typically be measured accurately and thus
obtaining strain as $\Delta L/L_{0}$ is straightforward. To obtain stress as
Force/Area, the surface area will be the smaller from the gripper jaws and the
side of the object. The crucial part, however, is the (compression) force. If
force is not directly available from the gripper, its calibration is necessary
(Section 4.3).

After collecting raw compression data on the robotic setups from both the
objects set and the polyurethane foams set, the mixed set of foams and cubes
was created (Section 4.1) and tested on a professional biaxial measuring
device (Section 4.4). The stress/strain curves are shown in Fig. 6. The curves
from the professional setup, Fig.6(d), will serve as reference. We observe
that the samples are clustered with the “Kinova cube” being the least elastic
material, followed by RL5045 and RP50080 foams. The rest of the samples occupy
the bottom of the plot. This clustering is apparent also on the data from the
RG6 gripper, Fig.6(b), and the FT300, Fig.6(c); it is less pronounced for the
2F-85 in Fig.6(a). The nonlinear response visible in the feedback recorded by
the professional setup is partially preserved in the plots from the other
devices. An important observation is the range on the y-axis. The absolute
values of stress differ significantly, which limits the possibilities of
estimation of the real value of the modulus of elasticity. The 2F-85 values
seem most in line with the professional setup; the FT300 is underestimating
the stress by approximately a factor of 2; the RG6, on the other hand, is
overestimating the stress by the same factor. For estimation of real values of
elastic moduli, such discrepancy is problematic.

Figure 6: Mixed set – stress/strain. (a) Robotiq 2F-85 gripper. Compression
speed 80 mm/s (50%). (b) OnRobot RG6. Discontinuous compression. (c) Robotiq
FT300 force/torque sensor. Compression speed 30 mm/s. (d) Professional setup.
Compression speed 50 mm/s.

###  5.3 Effect of compression speed and precycling

The ISO standard for low-density polymeric materials [18] prescribes that
samples be compressed at a speed of 1.67 mm/s and that the stress/strain
characteristics should be evaluated during the 4th compression cycle. To
assess the effect of these parameters, we first used the biaxial professional
setup. The compression and, in this case, also decompression curves for the
objects of the mixed set are shown in Fig. 7, (a)-(c). Note that the upper
part of every curve corresponds to compression. With higher speeds, the
difference between the compression and decompression curve (hysteresis) is
bigger. Individual compression cycles (1-6) do not have a significant effect
on the overall shape. Fig.7(d) shows how the estimated modulus varies at
different values of strain and with compression speed and cycle.

Figure 7: Compression and decompression cycles with different speeds on
professional device – mixed set. (a)-(c) Visualizations from biaxial
compression device – Force at one sensor over displacement of one jaw. Six
compression and decompression cycles for every speed and sample. (d) Variation
of estimated moduli with cycle number and speed, for the foam RP50080.

###  5.4 Young’s modulus

For the materials we tested, the stress/strain curves are nonlinear.
Therefore, the modulus of elasticity will be different at different points on
the curve. Thus, we estimate at different values of strain (0%, 5%, 40%, and
70%) by locally estimating the gradient, and a “linear” modulus that assumes
the whole curve is linear.

####  5.4.1 Estimating Young’s Modulus from robot gripper data

From the professional setup, we obtain on average 4000 points per compression-
and-release cycle. In comparison, the data from the robot grippers—OnRobot RG6
and Robotiq 2F-85—consists of only 200-300 points per cycle. Thus, the
feedback from the grippers is sparse and visibly discrete in nature. Further,
signal noise is significant. This noise may arise because of factors such as
rough initial contact and release or resistance from the opposite jaw. Hence,
prior to modulus estimation, the feedback is filtered using the Savitzky-Golay
filter which smooths data using least-squares polynomial fitting on smaller
window sizes. For the analysis of OnRobot RG6 data in this section, calibrated
force values (Section 4.3) are used.

To find the modulus at any chosen strain percentage, we create a neighborhood
around the strain value and find the slope of the best fit line in that
neighborhood using scikit-learn’s LinearRegression module. To ensure that the
best fit line obtained is actually representative of the slope at the chosen
point, we vary window sizes to obtain the highest $R^{2}$ correlation as a
measure. It is observed that this $R^{2}$ vs. window size variation is
consistent in shape for the modulus values obtained at 40% and 70% strains. As
shown in Fig.8(a), it can be seen that smaller window sizes have the highest
$R^{2}$ scores at 40% and 70% strain. Alternatively, the $R^{2}$ scores for
the best fit lines near the 0% and 5% strain values are very poor.

Figure 8: (a) Variation of $R^{2}$ scores with window size. (b) The best fit
line plotted for different window sizes. These are for cycle 5 of compression
of the foam RL5045, being compressed by the OnRobot RG6 gripper. Similar
curves were obtained for all foams.

The window size for our best fit lines was fixed at $\pm$ 10% strain on either
side. All results obtained from the robotic grippers are based on this window
size.

####  5.4.2 Estimating Young’s Modulus from Professional Setup

We calculate the modulus values from the data from the professional setup.
Modulus at 0%, 5%, 40%, and 70% was estimated using linear regression. Also, a
“linear” modulus was calculated for the entire curve. For one sample, RP50080,
statistical tests (t-test) were conducted to assess whether the compression
cycle or the speed affect the modulus estimation. For the moduli at 0%
($E_{0}$) and 5% ($E_{05}$), significant differences between cycle 1 and cycle
5 (p=0.01) were found. For $E_{40}$ and $E_{70}$, no significant differences
were found. Statistical tests comparing moduli estimation between slow speeds
(1-10 mm/s) and fast speeds (30-50 mm/s) were also conducted and no
significant differences were found. See also Fig. 7.

The moduli $E_{40}$ and $E_{70}$ moduli for the mixed set of samples are shown
in Table 3 (mean over compression speeds, first compression cycle only). The
error is presented as a ratio between the standard deviation and the mean.
Since the sampling was dense, approximately 2% window on both sides of the
desired strain value was sufficient.

Table 3: Mean values of 40 % modulus ($E_{40}$) and 70 % Modulus ($E_{70}$) for mixed object set on the professional setup; first compression cycle, all speeds. Foam |  $E_{40}$ [kPa] (Err) |  $E_{70}$ [kPa] (Err)
---|---|---
Blue die | 6.783 (10.0%) | 45.609 (15.2%)
Kinova cube | 82.638 (17.9%) | 82.638 (17.9%)
NF2140 | 9.756 (10.2%) | 46.047 (18.6%)
RL5045 | 26.323 (4.5%) | 116.240 (14.5%)
RP1725 | 6.391 (8.6%) | 20.557 (29.0%)
RP30048 | 12.439 (5.7%) | 50.479 (20.6%)
RP50080 | 20.044 (3.53%) | 75.912 (9.9%)
V4515 | 9.952 (27.32%) | 42.400 (30.68%)

####  5.4.3 Modulus estimation from all devices

Data from all the different devices and different settings were used for Young
modulus estimation on the mixed set sample. Estimations at 0% and 5% strain
are not reported here as these were hard to obtain in all but the professional
setup due to sparse sampling and presence of noise. At least five compression
and decompression cycles were performed with every setting and the moduli were
estimated at cycle 1 and cycle 5. Speed was varied for the professional setup
and for the Robotiq 2F-85 gripper. In addition, to account for the effect of
the surface area of the gripper jaws, the same pads (59 x 59 mm) used in the
professional setup were mounted onto the OnRobot RG6 and Robotiq 2F-85 jaws as
an additional setting.

The results of Young modulus estimation at 40% strain are shown in Fig. 9. The
green bars in every subplot are from the professional setup and serve as
reference. The following observations can be made: (1) no robotic device
provides an accurate and reliable estimate of Young’s moduli corresponding to
the values obtained from the professional setup; (2) adding the pads and thus
increasing the surface area for the 2-finger grippers brings the absolute
values closer to the reference, but adds noise to the estimation (disrupting
the relative ordering of samples by elasticity); (3) the FT300 force sensor
provides the most stable estimation, albeit the absolute values of Young’s
modulus are significantly lower compared to the reference. This is consistent
with the raw strain/stress curves in Fig. 6; (4) there is no clear effect of
precycling (5th versus 1st compression cycle); (5) bigger compression speed
degrades the estimation for the Robotiq 2F-85 gripper.

Figure 9: Mixed set – Young modulus at 40% strain. Estimation using different
devices and settings.

####  5.4.4 Linear modulus and relative elasticity estimation

The previous sections have shown that the capability of robotic grippers to
deliver accurate estimates of Young modulus at different strain values are
limited. Due to noise and limited resolution of the devices, local windows for
estimation at e.g. 40% and 70% are unreliable. From a practical point of view,
relative discrimination of objects based on their elasticity will often
suffice. After experimentation, we propose to measure the stress/strain ratio
over the whole compression area. This assumption is not correct since the
mechanical response curves are clearly nonlinear, but it provides stable
results in terms of ordering the samples by their elasticity, largely
consistent across the different devices – see Fig. 10 and below:

$KinovaCube>RP50080,RL5045>V4515,\\\ RP30048,NF2140>RP1725,BlueDie$ (8)

Figure 10: Linear modulus for each foam obtained by different grippers,
compression speed = 1.6mm/s. Please note the different scale on the y-axes.

###  5.5 Viscoelasticity and the hysteresis loop

All the materials composing the mixed set have hysteresis loops (explained in
Section 3.2.1) as can be seen in Fig. 7. The amount of energy lost is shown to
be linearly proportional the compression speed in Fig. 11. The linear
coefficient of the energy lost vs. speed graph is a characteristic of the
material, and we label it $\eta$. The values of this energy loss coefficient
obtained from the professional setup are listed for all materials in Table 4.
The materials fall approximately into two groups based on the values of
$\eta$. The viscous component is pronounced for the Blue die, Kinova cube, and
the V4515 polyurethane foam. The Blue die and Kinova cube differ from the
foams in that they are not completely homogeneous—they have a smooth outer
shell that encloses the inside of the material and changes the properties. The
difference in viscosity of the polyurethane foams may have to do with their
porosity. Viscosity can provide and additional dimension next to elasticity to
improve discrimination of soft materials.

Figure 11: Viscoelasticity – mixed set. Variation of the amount of energy lost per compression and release cycle with different speeds. Table 4: Viscoelastic coefficient obtained by calculating the hysteresis energy loss for multiple speeds on the professional setup. Foam |  $\eta$ (x $10^{3}$)[N.s.$m^{-2}$]
---|---
Blue die | 24.717
Kinova cube | 119.487
NF2140 | 3.267
RL5045 | 6.314
RP1725 | 5.392
RP30048 | 2.960
V4515 | 45.812

###  5.6 Measuring viscoelasticity with Robotiq 2F-85 gripper

All the models to characterize the viscous characteristics of the samples
introduced in Section 3.2—area inside the hysteresis loop, Kelvin-Voigt model,
and Hunt-Crossley model—were applied to the mixed set samples as measured by
the Professional setup and the Robotiq 2F-85 gripper.333Note that the OnRobot
RG6 gripper cannot be used since continuous object compression with different
speeds while recording force feedback is not possible. Both devices were used
to compress and release the samples with the following speeds: 1.6, 30, 50, 80
mm/s. To find parameters of the Kelvin-Voigt model and the Hunt-Crossley
model, data from the first and fifth cycles for different speeds was fit into
Eqn. (3) and Eqn. (4) individually and then averaged.

An overview of the results is in Fig. 12. The correspondence between the
viscosity/damping parameter obtained from the professional setup and from the
Robotiq 2F-85 gripper is not satisfactory for the area inside the hysteresis
loop ($R^{2}=0.46$) and the Kelvin-Voigt model ($R^{2}=0.35$) is not
satisfactory. Only the Hunt-Crossley model ($R^{2}=0.81$) provides a
reasonable correlation—we will thus use this model in what follows.

Figure 12: Comparing viscoelasticity ($\eta$) values obtained from the
Professional Setup (left) and the Robotiq 2F-85 gripper (right).

###  5.7 Material discrimination from elasticity and viscoelasticity

Given the limited capabilities of robotic grippers to gauge material
elasticity (Sec. 5.4) and viscosity (Sec. 5.6) alone, if the goal is online
discrimination of deformable objects, it is advantageous to use both these
quantities simultaneously. This is visualized in Fig. 13 with the values
obtained from the professional setup and the Robotiq 2F-85 gripper side by
side. One can observe that there is a good qualitative match between the two
measuring devices and that the second dimension importantly aids the
possibility of discriminating the objects. Performing actual classification is
not in scope of this work but it is straightforward.

Figure 13: 2D object discrimination – elasticity using the linear assumption
(Sec. 5.4.4) on x-axis and viscosity as obtained from the Hunt-Crossley model
($\eta$ Eqn. 4) on y-axis. (Left) Professional setup. (Right) Robotiq 2F-85.
Clusters formed are marked by hand.

##  6 Conclusion, Discussion, Future Work

Robot grippers are primarily designed for grasping rather than for haptic
estimation of material properties. However, if they could be employed for
object discrimination by only squeezing and releasing a sample, it would have
important application potential in areas like food handling and single-stream
garbage sorting. In this work, we employ two standard industrial robot
grippers with force feedback and, for comparison, a force/torque sensor at the
robot wrist to press objects against the table. A sample of ordinary cube-like
soft objects and a challenging set of polyurethane foams from a mattress
manufacturer are tested. A subset of the objects is tested on a professional
setup to provide control values.

In terms of gauging stiffness/elasticity, we found the following: (i) the
robot grippers, even after calibration of the force feedback, were found to
have a limited capability of delivering accurate estimates of absolute values
of the modulus of elasticity (Young’s modulus) at different compression
levels; (ii) precycling—measuring elasticity not on the first compression
cycle but on the fourth or fifth as recommended by standards [18]—did not have
a significant effect and hence data from the first compression cycle can be
directly used; (iii) slower compression speeds are advantageous for
estimation; (iv) relative ordering of the samples, is possible and largely
consistent across the devices. Although the mechanical response stress/strain
curves of the soft objects are nonlinear, in practice it proved more accurate
not to attempt fitting gradients and estimating Young’s modulus at different
compression levels. Instead, fitting a single straight line over the whole
compression path gave the most stable results.

Soft objects are typically viscoelastic—energy is absorbed in a compression
and release cycle. The viscosity, or damping, is dependent on compression
speed. These characteristics can also be extracted provided that force can be
measured during compression as well as release of the sample. Obtaining data
from different gripper nominal speeds improves the estimation. In our case,
the Hunt-Crossley model proved the most accurate.

In terms of the robot devices we tested, the Robotiq 2F-85 gripper is limited
in its sampling rate, but it has the important capability to be able
continuously measure the effort during a compression and release cycle. The
effort is in motor current (A) and calibration is necessary to obtain force
(N) to estimate the elastic modulus in real physical units. However, even
after calibration, such estimation was not accurate. On the other hand, if
only relative ordering or discrimination of viscoelastic objects is desired,
this device will suffice. The OnRobot RG6 can only measure force when a set
threshold is exceeded. The threshold then needs to be reset to continue
compression. Such measurement is slow but sufficient to coarsely estimate
material elasticity. However, the fact that no measurement during releasing is
possible and that speed cannot be varied makes the measurement of
viscolelasticity impossible. For comparison, we also show data from pressing
an an object with the robot flange and measuring the resistance with a force
sensor at the manipulator’s wrist. This proved accurate but may not be
applicable in many situations when grasping an object is needed simultaneously
with elasticity measurements.

Overall, this work provides a systematic investigation of the feasibility of
online haptic discrimination of soft objects based on their viscoelastic
properties using standard robot grippers. We provide guidelines, code, and
dataset. A 2-finger parallel jaw gripper capable of measuring effort during
compression and decompression of the sample is capable of discriminating
deformable objects. We show that this is possible even for a challenging
sample set like 20 similar polyurethane foams. Combining elasticity and
viscoelasticity estimation is advantageous. For this, a couple of
compression/decompression cycles at different gripper speeds works best. All
the processing we used—detecting contact, obtaining the stress/strain curve,
estimating elasticity, and fitting a Hunt-Crossley model—is white-box, simple
(compared to finite element method modeling or to deep neural networks), and
can work online. In the future, it can be complemented with existing visual-
based methods. The viscoelastic properties perceived can be further used to
devise appropriate manipulation policies [33, 14].

##  7 Declarations

Funding This work was co-funded by the European Union under the project
Robotics and advanced industrial production (reg. no.
CZ.02.01.01/00/22_008/0004590). Hynek Chlup is funded under grant no.
GA23-06920S by the Czech Science Foundation (GA CR).

Competing Interests Not applicable.

Availibility of Data and Material All raw data is made available in our public
data repository.

Code Availibility Code for the analysis of data is made available in our
public code repository.

Ethics Approval Not applicable. Consent to Participate Not applicable. Consent
for Publication Not applicable.

Author Contributions All authors contributed to the study conception and
design. Material preparation, data collection and analysis were performed by
Shubhan P. Patni and Pavel Stoudek. The first draft of the manuscript was
written by Shubhan P. Patni and Pavel Stoudek and all authors commented on
previous versions of the manuscript. All authors read and approved the final
manuscript.

Acknowledgements We would like to thank Karla Stepanova for her inputs, and
Bedrich Himmel for assistance with gripper calibration.

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