## 5 Conclusions  
In-hand manipulation with force-control-based pushing primitives is formulated and implemented to achieve the precise placement of bushings in a machine slot, even under conditions that make it difficult to grasp from a planned position. To avoid difficulty in the mathematical modeling of friction between the fingertips and grasped objects, we adopted a strategy that places the gripper at the edge of the grasped object by exploiting prehensile pushing actions using an external environment, regardless of the initial grasping position. Therefore, detecting and maintaining the contact force between the gripper and the external environment is of primary importance and can be accomplished by force feedback control. As external forces are estimated by joint torque sensing, additional sensors, such as vision or tactile sensors, are not necessary.  
A smoothing function was introduced to effectively create slip between the fingertip and the object at the start of pushing that used a step-based form of interaction force, and to smoothly conclude the interaction between the gripper and the external pusher at the end, a ramp-based form of interaction force was used. The experimental results demonstrated the feasibility of the proposed method, showing that the bushing object could be precisely placed into the machine slot despite variations in initial grasping positions. Compared to other methods, such as the no-pushing approach and the planning pushing approach, which achieved only a 33% success rate, our proposed method achieved a significantly higher success rate of 97%.  
Our proposed method leverages a feedback loop and an external pusher, which implies that it does not require an accurate friction model. More importantly, this approach allows the force controller for the pushing axis to be implemented using traditional PID or LQ control techniques as well as heuristic approaches [40, 41]. As a result, our approach demonstrates the feasibility of automating industrial processes without the need for complex control methodologies, which is a significant advantage.  
The authors' ongoing research is into integrating the grasping process, which includes recognizing an object's pose by utilizing a vision sensor fixed at the wrist of the manipulator, and expanding their research to various types of objects. Data-driven techniques for estimating frictional force during pushing manipulation will also be considered to address various uncertainties, such as surface inconsistencies or the presence of debris, and maximize automation.  
**Author Contributions:** Conceptualization, J.P., J.-J.K., and D.-Y.K.; methodology, J.P. and J.-J.K.; software, J.P. and J.-J.K.; validation, J.P. and D.-Y.K.; formal analysis, J.P., J.-J.K., and D.-Y.K.; investigation, [PERSON]; resources, [PERSON]; data curation, J.-J.K. and D.-Y.K.; writing original draft preparation, [PERSON]; writing review and editing, [PERSON]-J.K. and D.-Y.K.; visualization, [PERSON]; supervision, [PERSON]; project administration, J.-J.K.; funding acquisition, [PERSON] All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported by the National Research Council of Science & Technology as part of the project entitled \"Developed core technologies for the Robotic General Purpose Task Artificial Intelligence (RoGeTA) framework to enable a variety of everyday services\" (NK248G) and the Industrial Strategic Technology Development Program (no. 20018745 and no. 00416440) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflicts of interest.