# Scattering or Pushing for Object Singulation in Cluttered Environment: Case Study with Soma Cube
## 2 Methodology  
In this paper, both non-prehensile and prehensile manipulations will be used to achieve object manipulation in cluttered environment. Soma cube will be used as an example to show the effectiveness of the proposed technique. The Soma cube is a three dimensional puzzle as shown in Figure 1, having seven blocks, made up of 27 cubes. Six blocks are made up of four cubes and one block is made up of three cubes. They are used as the building blocks to assemble them for achieving desired target formation. There are various ways in which these blocks can be assembled such as a cube or several 2D or 3D formations. Scenario is as follows. Initially, we assume that 7 blocks of the Soma cube are cluttered together in a formation. For grasping blocks safely without colliding with other pieces, singulation of blocks placed on the table should be proceeded first. Considering pros and cons of the quasi-static singulation and the dynamic singulation, we would like to adapt the following strategy: hybrid approach for efficient object singulation and safe object manipulation. (i) Step 1: Dynamic singulation approach by scattering  
Purpose: separation of objects in short time to make the size of cluster * smaller  
(* cluster: a group of blocks that are too close to each other for grasping)  
(ii) Step 2: Quasi-static singulation approach by Pushing  
Purpose: separation of objects in small cluster group Figure 2 explains the flowchart of the proposed hybrid singulation approach in detail. Initially, several blocks of Soma cube are laid on the table as shown in Figure 3a. Then, scattering is performed to separate the blocks in a desired manner. Here, the desired manner means scattering all the blocks such that the robotic gripper is able to grasp each block in a safe manner without collision with other blocks remaining on the table. However, just by one time scattering, there is no guarantee that all the blocks can be scattered in a desired manner enough to conduct prehensile manipulation by the robot hand. Figure 1: Soma cube. (**a**) Seven blocks (**b**) Different formations. Figure 2: Hybrid Singulation Manipulation. It is probable that a small cluster group consisting of two or three blocks of Soma puzzle may exist even after scattering. In order to complete the singulation of all blocks, we use pushing as the secondary singulation method. It is, however, noted that before conducting pushing we should perform prehensile manipulation to remove blocks that are obstructing the path of the manipulator when pushing is carried out as shown in Figure 3b. After the desired separation is achieved by pushing, prehensile manipulation is conducted for the remaining pieces. As explained in the proposed approach, the prehensile and non-prehensile manipulation methods are combined for effective robot grasping and manipulation of blocks in cluttered environment. Furthermore, in order to implement non-prehensile manipulation such as dynamic and quasi-static methods, we need to identify the dynamic characteristics of blocks and the environment. Based on these properties, a virtual world simulator is designed to perform the object singulation. The virtual world simulator is designed based on the proposed impulse based dynamic model. In the virtual world, first of all the point of contact (i.e., where to hit), the piece to hit, and the direction of velocity are decided. Under this condition, the velocity of manipulator is controlled based on the feedback error (i.e., the distance error between the pieces) until the desired object singulation is achieved. In the virtual world simulator, the colliding velocity of robot and direction of collision is updated by employing a feedback routine to minimize the error to achieve the desired singulation pattern. The physical properties of the blocks such as masses, coefficient of restitutions between blocks, and coefficient of friction between blocks and the ground are estimated based on the technique proposed by [PERSON] et al. [15].