@[toc](Contents) ## Introduction ## This dataset is a collection of force and displacement time series data collected by the [Humanoids and Cognitive Robotics Lab][1] at [Czech Technical University in Prague][2]. The data is collected on a set of deformable objects with the aim of estimating the mechanical properties of the material - specifically the Young's modulus (or modulus of elasticity) $E$ and the coefficient of viscoelasticity $\eta$. The set of deformable objects comprises of two cubical objects and six cuboidal foam pieces.  The foams are a portion of a larger set obtained from https://www.molitany.com/. The dimensions for each object are provided below: |Object|Dimensions (mm)| |-------------|----------| |Blue Die| 90x90x90 | |Kinova Cube| 56x56x56 | |NF2140| 105x100x50 | |RL5045| 118x118x39 | |RP1725| 118x120x41 | |RP30048| 123x121x39 | |RP50080| 121x118x39 | |V4515| 118x120x40 | ## Data Collection ## 1. Professional Setup: The first set of data was collected from a professional setup housed at the [Division of Biomechanics][3]. A biaxial Zwick/Roell system is used to compress and release each test object for multiple cycles at multiple speeds (1.6, 10, 30, 50 and 80 mm/s). The mechanical parameters obtained from this data are used as the true values, and the estimates from each gripper are compared to these control values. Here the Blue Die is denoted by K1 and Kinova Cube by K2.    2. Robotic Grippers: The force and displacement response from three different robot grippers was recorded. The idea is to see how accurately the value of the mechanical properties $E$ and $\eta$ can be estimated. The different grippers used are: -The Kinova arm with the Robotiq 2F-85 gripper: The 2F-85 gripper records the force feedback as a current value between 0 and 1 Ampere. This value had to be calibrated with the help of a ClipX sensor. -The UR10e Robot with The OnRobot RG6 gripper -The UR10e Robot with the Robotiq FT300 Force-Torque sensor Both the grippers paired with the UR10e record force feedback in Newtons. Another major difference between the three grippers is that the 2F-85 and FT300 grippers can complete the compression and release cycle in a continuous manner. However the Onrobot RG6 gripper only compresses continuously, its release motion is instantaneous. ## Filtering and Calibration ## The data obtained from all the grippers is noisy and does not have the same precision as the professional setup. While the professional setup has around 3000-4000 data points per compression cycle, only 300-400 data points per cycle are available from the grippers. Further, the least count for the RG6 gripper is a 1N, and for the 2F-85 gripper it is 0.01A. The Savitzky-Golay filter was used to smooth the feedback obtained from all the grippers. 1. OnRobot RG6: The force feedback from the RG6 gripper was calibrated by giving it a target force threshold and then measuring the actual force exerted by it on the ClipX sensor. The correlation between measured force and actual force was obtained as: $F_{Real} = 0.8678 \times F_{RG6} - 2.13$  2. Robotiq 2F-85: The 2F-85 gripper force feedback in milliAmperes of current consumed by the gripper motor. The conversion from current to force was obtained by programming the gripper to apply force on a target foam at a constant speed and collecting feedback from the gripper and the ClipX sensors attached to the foam's surface. $F_{Real} = 87.6i^3 - 216.0i^2 + 191.4i + 0.18$  Both the plots are for the foam: RP30048 ## Elasticity Estimation ## Estimating the modulus of elasticity for rigid materials is a simple task. Their stress-strain curves are usually a straight line, so the modulus or characteristic value of the material is defined as the slope of that line: $E=\frac{F/A}{\Delta L/L_{0}}$ Where $E$ is the modulus of elasticity, $F$ is the applied force, $A$ is the area under compression, and $\Delta L$ is the change in the original length $L_{0}$ due to the compression. It is comparitively difficult for the target objects of this dataset - deformable objects - that have a non-linear response when compressed and released. For this dataset, we focus on two possible methods for obtaining a value of the modulus of elasticity. The first method is to measure a localised modulus at chosen strain percentages. The second option is to assume the curve to be linear and obtain a single modulus for the entire curve. All values are estimated by choosing a region on the curve and fitting all the data points within that region on to the straight line equation. The slope of the line gives the modulus. The scikit-learn LinearRegression modulus is used for the purpose of fitting. 1. Localised moduli: The strain percentages chosen to estimate the local modulus around were 0% (Immediate force change upon contact), 5%, 40% and 70%. The size of the local window was optimized by minimizing the regression error. We observe that across different speeds and multiple cycles, the variance is least for the 40% and 70% modulus estimates, as observed in the figure below.  2. Linear modulus The 'linear' modulus assumes tries to fit the compression part of stress-strain response into a straight line. This method gives up theoretical agreement to make practical results more consistent. The results are presented below. While the absolute values are still inaccurate, we can see that a relative order of the estimates emerges in the cases where the 'pads' have not been added to the grippers: $Kinova Cube > RP50080, RL5045 > V4515, RP30048, NF2140 > RP1725, Blue Die$  ## Viscoelasticity Estimation ## The nonlinear behaviour in soft objects arises because their internal structure is not rigid. Instead, it is stacks of layers that are slightly free to move with respect to each other. Movement causes friction between the layers and results in energy loss when the object is compressed/released. This energy loss phenomenon is known as elastic hysteresis. It is an important property of materials. There are many mathematical models that can be used to represent nonlinear behaviour. we have explored the Kelvin-Voigt Model and the Hunt-Crossley model. The Hunt-Crossley model was able to give the best results in terms of maintaining the relative order of estimated viscoelasticity across different grippers. It expands upon the simple second-order spring-damper model by adding nonlinear power terms to the stiffness and damping components. The modified equation is: $F(x(t),\dot{x}(t))=Kx^{n}(t) + Bx^{n}(t)\dot{x}(t)$ $F$ is the applied force, $K$ is the stiffness/elasticity parameter, $B$ is the damping/hysteresis parameter, $x$(t) and $\dot{x}$(t) are the deformation and rate of deformation respectively. 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. Once a cycle of compression and release data has been collected in the form of deformation and force feedback, it is fit into the above equation using multi-variable linear regression to obtain values of $K$ and $B$. Since it is an exponential, instead of fitting data on this equation we fit data on the logarithmic form.  ## 2D Grid Classification ## Using the estimated value of the linear modulus and viscoelasticity, we are able to group our object set on a 2-dimensional grid. This process will further help in characterizing, grasping and manipulating unknown future objects because exploratory and manipulation actions can be decided based on which region of the grid the unknown object lies in.  ## Acknowledgements ## This work was supported by the project Interactive Perception-Action-Learning for Modelling Objects (IPALM) (H2020 -- FET -- ERA-NET Cofund -- CHIST-ERA III / Technology Agency of the Czech Republic, EPSILON, nr. TH05020001). S.P. was additionally supported by the Czech Technical University in Prague, grant No. SGS20/128/OHK3/2T/13. M.H. was also partially supported by OP VVV MEYS funded project CZ.02.1.01/0.0/0.0/16\_019/0000765 ``Research Center for Informatics''.   We would also like to thank our contributors Pavel Stoudek for help with data collection and robot programming, Hynek Schlup for his assistance with material testing and theory, Karla Stepanova for inputs to the early stages of this work, and Bedrich Himmel for assistance with gripper calibration. [1]: https://cyber.felk.cvut.cz/research/groups-teams/humanoids/ [2]: https://www.cvut.cz/en [3]: https://fs.cvut.cz/en-ustavy/en-section-department-of-mechanics-biomechanics-and-mechatronics/en-department-of-mechanics-biomechanics-and-mechatronics-12105/en-department-12105/