## 4 Conclusions  
In this paper, we proposed a cooperative human-robot interface for robot-assisted endoscopic endonasal surgery based on a hybrid concept of a force based and a serial-link interface to enhance intuitiveness and safety during highly dexterous anatomically constrained surgical tasks in EES. First, the surgical task was divided into stages, each of which was concerned with specific challenges and constraints. A force based interface was chosen for positioning, insertion, and extraction of the articulated forceps because of the simplicity and natural control arising from human-robot physical interaction. During the positioning stage, the robot worked in gravity compensation mode and followed the force applied by the surgeon over the interface. Then, the robot constrained the forceps motion along a virtual remote-center-of-motion fixed in the nostril during the insertion and extraction states. Once the tool was placed at the target workspace, we used a serial-link interface for precise control of the articulated forceps while keeping a virtual remote-center-of-motion at the nostril. Workspace constraints were implemented based on virtual fixtures to limit the tool workspace and ensure safe motion inside the patient. We defined the constraints from a phantom head to determine the sinus cavity and the dura workspace. We proposed a state based real-time controller that combined an admittance controller for positioning and insertion/extraction with a position tracker to control the forceps tip during the surgical task, ensuring smooth transition between these stages. Finally, we compared the performance of our proposed system with the use of conventional surgical instruments in common surgical tasks. A reachability experiment in a phantom head showed the capability of reaching the areas of interest such as the pituitary area in a smooth and precise way compared with the use of conventional instruments. Pick-and-place and block-in-hole experiments were performed to evaluate the manipulation of objects inside the nasal cavity under the anatomic constraints imposed by the nostril. The results showed a noticeable improvement in the motion smoothness. In addition, a needle stitching task was conducted to test the system in the highly dexterous surgical task. The robotic system showed a similar time for each phase, with a high reduction in the Regrasping phase, where passing the needle was challenging with the requirement of keeping a proper needle orientation. The same experiment showed a reduction in the force distribution applied over the tissue during the needle insertion/extraction. The results demonstrated that the proposed system could control and safely constrain the motion of bimanual robot arms with articulated multi-DOF forceps for endoscopic endonasal surgical tasks. Future work will focus on implementing optimization algorithms to generate a constrained trajectory that tracks the user interface motion during a complete multi-throw suturing sequence.  
Conceptualization, J.N. and Y.H.; methodology, J.C.; software, J.C.; experiments, J.C.; writing, original draft preparation, J.C.; writing, review and editing, J.N., T.A., and Y.H.; supervision, J.N., T.A., and Y.H.; project administration, Y.H.; funding acquisition, Y.H. All authors read and agreed to the published version of the manuscript.  
This work was funded by the ImPACTProgram of the Council for Science, Technology and Innovation (Cabinet Office, Government of Japan).  
Figure 19: Needle stitching sequence.  
**Acknowledgments:** We thank [PERSON] at the University of Tokyo for his assistance with the real-time control implementation and [PERSON] at Denso Corporation for his help with the robot hardware setup.  
**Conflicts of Interest:** The authors declare no conflict of interest.