# Robotic Assembly for Irregular Shaped Peg-in-Hole with Partial Constraints
## 4 Experiment
### Hole Searching and Insertion  
After the alignment process, the key and shaft parts are steered at a fixed position and posture. Therefore, the slot-key assembly can be performed afterward. The following steps are required to complete the process:  
1. Change the slot part posture to vertical posture and let the hole face downward;
2. Drive the slot part to a skew state and make sure the bottom edge is below the top surface of the key part (According to physical parameters and (6), \(h=1\) mm);
3. Move the slot part toward the key until contact and keep contact during the searching process;
4. Rotate the slot around the contact edge in a counterclockwise direction using the force control policy (10) until the slot is jam with the key;
5. Complaintly insert the slot into the key using force control policy (11). Figure 14 shows the snapshots during the hole searching and insertion process. In Figure 14a, the part was reoriented to a pre-search skew posture; In Figure 14b, the slot is in contact with the key and ready to perform a circular searching action; In Figure 14c, the key has been critically inserted into the slot hole and it is ready to perform the final insertion. When all above assembly operations have been completed, the experimental data shows in Figure 15. The trajectory of the robot end-effector was shown in Figure 15a. As the figure shown that four stages of the assembly were presented explicitly. The three directions force were shown in Figure 15b. The force change along the \(X\) and \(Z\) axes denote the different assembly stages. Figure 14: Key-slot hole searching and insertion process. (**a**) pre-insertion stage; (**b**) hole-searching stage; (**c**) insertion stage. In the posture regulating and pre-insertion process, the control system switches the force control mode. As Equations (8) and (9) denote, the direction of force controlling is along the \(Y\)-axis of the workpiece's frame. In the hole searching stage, the two directions of impedance control are along \(Y\)-axis and around \(X\)-axis. The robot posture is illustrated in Figures 13 and 14. Posture regulation is a \(Z\) direction force control process, and the hole searching is an impedance control process along the \(X\) and \(Z\) directions, respectively. Figure 16a shows the \(Z\) trajectories and force value along the \(Z\)-axis. It explicitly illustrates the changing of the force and the trajectories according to the assembly stage. The \(X\)-axis trajectories and contact force is shown in Figure 16b. It mainly describes that the force changes in the pre-insertion and searching stage, respectively. To validate the repeatability and reliability of the proposed method, the above assembly operations are repeated five times. The simultaneous regulation stage is the most important stage in this experiment. The hole searching and insertion stage will succeed only if the simultaneously regulation is successful. The initial position and posture of the key-shaft component in snapshots shown in Figure 17a. The robot using force control along \(Y\)-direction in the simultaneously regulates the posture of key-shaft component. Figure 17a illustrates that the key-shaft component have a different initial position and posture. When the robot finishes the simultaneously regulation stage, the position and the posture of the key-shaft component has been aligned to the same position. Figure 17b shows the initial and final position of the robot end-effector in the regulation stage and the aligned posture from five experiments is shown in Figure 17c. Figure 17 shows that the initial position and posture errors of the key-shaft component will be corrected after the simultaneously regulation stage. The key-shaft component is aligned to a stable posture. The proposed method is tested in different situations and shows very good repeatability. Figure 15: The trajectory and force of key-slot assembly. (**a**) The robot trajectories of the assembly task; (**b**) the force value in different time step. Figure 16: The trajectory and force of key-slot assembly.