## 4 Experimental Evaluation
### Mock-Up Tests  
The mock-up hardware represents the bushing machining process, as shown in Figure 6. The machine slot is placed in front of the robot manipulator, and the clearance of the slot is 5 mm, which allows for placement only when the bushing is well positioned. In practice, the bushing is supposed to lie in the bin randomly. However, in this paper, to focus on the problem of placing the bushing in the desired posture, we used a fixed jig to adjust the bushing grasping position arbitrarily to exclude the posture recognition problem (see Figure 7). Although not included in this paper, well-known artificial intelligence (AI)-based algorithms, such as the region-based convolutional neural network (R-CNN), could be possibly useful methods for recognizing the posture of the target bushing. Figure 6: Experimental configuration established to demonstrate real process. Figure 7: Various grasping positions can be manually adjusted with a jig to express imprecise grasping situations (the yellow dashed lines represent the gripper). Figure 8 shows the sequences of grasping and placing scenarios that use a Cartesian-force-control-based pushing action. The initial grasping position is manually adjusted to the long and short position of the bushing using a jig. The gripper is located at the end of the bushing in both cases so that placing in the slot is achievable. The left side of the slot is adopted as an external pusher; by doing so, the tac time for the next operation, inserting the bushing into the machine slot, can be minimized. The graphs Figures 9 and 10 represent the detailed results seen during the period from before pushing to finishing. In the pushing period, the position reference is set to a point through the slot in the Y direction. The robot arm begins to approach the external environment (the left side of the slot) with a straight-line trajectory (+Y direction in global coordinates) at 6.3 s (indicated by black dotted vertical line). The entire control input is significantly increased from 7.3 s to 7.7 s because the position controller cannot reduce the position error, which occurs due to contact between the bushing and the slot; the third column of Figure 8 shows this situation. The external contact force is measured by joint torque sensing and the inverse of the Jacobian transpose, \(F_{e}=J^{-T}\tau_{e}\), as shown in Figure 10. When the external force exceeds the threshold, the force control trigger is enabled, and the control state is changed to the force controller. The desired force of the controller, which is the same magnitude as the trigger threshold, is set to 13 N experimentally to consistently make slip occur between the gripper and the bushing. The position control input disappears, and the force controller maintains the contact force. The aim is to position the gripper at the end of the bushing and there is a fixed pusher at that point, so the magnitude of the force can be quite robust. The behavior of the position control input and the force control input, as shown in Figure 9, represent the characteristics of the smoothing function. To ensure a clear slip between the gripper and the object at the beginning of the pushing phase, the position control input disappears in a step-wise manner, while the force control input is applied in a step-wise fashion. As seen throughout the entire control input, unstable phenomena such as discontinuities rarely occur, and it can be observed that pushing proceeds stably through force control. Conversely, when pushing ends, the force control input decreases in a ramp shape, as shown in Figure 9. Once the force control input completely disappears, the position control input takes over and performs the next operation. Figure 8: Experimental sequences from imprecise grasping to precise placing into a slot. The two different grasping positions represented are the long grasping position in the top row and the short grasping position in the bottom row. The snapshots were manually chosen to show the highlighted moments.