# Singulation of Objects in Cluttered Environment Using Dynamic Estimation of Physical Properties
## 5 Scattering Algorithm and Experimentation  
In this section, the developed analytical methodology is verified by performing the scattering experiments. We use six different objects with distinct physical properties, such as mass, coefficient of restitution, coefficient of friction, and shape, for object singulation experiment. The objects singulation is performed based on the proposed scattering algorithm. Once all the physical properties of the objects are identified, we can integrate them in a physics engine to design a virtual world simulator to perform controlled scattering. We conducted scattering experiments in the virtual world to scatter objects in a desired manner. First of all, it is necessary to define a scattering index that can be used as a measure of scattering performance. Here, we need to provide some constraints to the scattering task:  
1. Initially, we assumed that all objects are placed together. 2. The distance among objects after scattering does not go beyond the given workspace. Maximum and minimum distances \((S_{\text{min}},~{}S_{\text{max}})\) are given. 3. Hitting strategy: Among objects, the first priority is to hit the largest object in the cluster for an initial collision to scatter all objects. The reason for hitting the largest object is to provide enough impulse to drive out other smaller objects. 4. How to hit the largest object: This is based on a central impact to simplify the number of parameters. Other than that, the number of parameters needed to estimate the physical properties are increased. 5. Magnitude of the velocity: In terms of deciding the magnitude of colliding velocity, it is based on the scattered distances among objects. We conducted simulations several times until all objects satisfied the condition of scattering. 6. Direction of the robot motion: The direction of robot motion is selected considering the ability of the manipulator to generate impulse in certain direction. [PERSON] et al. (2016) proposed the normalized impact geometry to analyze the impulse generation ability of the manipulator. Figure 10 shows the generalized impulse geometry for the robot manipulator, which is constructed based on the impulse model of Equation (8). Figure 10b,c shows the maximum and minimum impulse direction for four different configurations. The direction of robot motion is decided to apply the maximum impulse. However, in some cases the largest object is surrounded by other objects in clutter and not accessible for initial collision with the robot manipulator. In this scenario, the direction of robot motion is decided to maximize the external impulse without considering the constraint (iii). 7. The scattering index is set as the average distance among objects. It can be expressed as: \[s_{\text{min}}\leq\sum_{i=1}^{M}\sum_{j=i+1}^{M}\frac{\|\mathbf{r}_{i}-\mathbf{r}_{j} \|}{N}<s_{\text{max}},\text{where }N={}_{M}C_{2},\] (35) subject to the distance constraint between objects \(i\) and \(j\): \[\|\mathbf{r}_{i}-\mathbf{r}_{j}\|\geq d_{\text{min}}(i\
eq j),\] (36) \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Objects** & **ma/ma** & **ma/mb** & **ma/mc** & **ma/md** & **mb/mb** & **mb/md** & **mc/mb** & **mc/md** & **ma/me** \\ \hline Error \% & 3.47 & 6.15 & 4.8 & 6.9 & 1.7 & 10 & 2.5 & 6.5 & 3.13 \\ \hline Objects & me/mb & mc/me & me/md & ma/mf & mf/mb & mc/mf & mf/md & me/mf \\ \hline Error \% & 7.7 & 2.91 & 0.79 & 8.75 & 5.98 & 1.05 & 3.14 & 6.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Percentage error between mass ratio of the true value and the estimated value. where \(\mathbf{r}_{i}\) is the mass center of \(i^{th}\) object in plane. \(N\) and \(M\) are the number of objects and the number of connection of objects, respectively. Equation (35) implies the average distance among all objects and Equation (36) implies that distance between two consecutive objects should be grater or equal to \(d_{\text{min}}\). The additional constraint of Equation (36) is included to make sure that all objects are apart from each other.