# Human-Robot Cooperative Control Based on Virtual Fixture in Robot-Assisted Endoscopic Sinus Surgery
## 5 Conclusions  
This paper proposed a human-robot cooperative control method based on VF to improve the accuracy and safety of surgical operation in robot-assisted endoscopic sinus surgery. Firstly, based on the analysis of endoscopic motion constraint requirements in different surgical stages, three typical VFs suitable for endoscopic sinus surgery were designed and implemented. The GVF based on a spatial curve was designed to achieve motion guidance from the nasal cavity entrance to the operating area. Considering the funnel-shaped workspace of the endoscope, the FRVF based on the single-leaf hyperboloid was designed to achieve motion constraints at the entrance to nasal cavity. The FRVF based on the anatomical structure of the nasal cavity was designed to constrain the motion of the endoscope inside the nasal cavity, the boundary of which coincides with the boundary of the nasal tissue, thereby maximally retaining the precious operation space while protecting the nasal tissue. Thereafter, a composite VF was constructed based on the above typical VFs, and an overall robot motion constraint model was obtained. Secondly, based on the obtained robot motion constraint model, a human-robot cooperative control method based on VF was proposed. The method adopts admittance-based control to realize efficient human-robot interaction between the surgeon and robot during surgery, and the surgeon adjusts the endoscope to the desired posture by dragging the end of the robot. During the dragging process, the motion of the robot is restrained and guided by the VFs to prevent the endoscope at the end of the robot from interfering with the nasal tissue. With the proposed control method, the surgeon can free his left hand and carry out complex surgical operations with both hands, thus improving operation efficiency. Finally, validation experiments were conducted. The GVF experiment based on the cubic polynomial curve was performed and the results showed that the proposed GVF can effectively reduce the trajectory tracking error of the robot and improve the drag operation precision. The composite FRVF based on the spatial plane and a single-leaf hyperboloid was tested and the results showed that the proposed FRVFs can prevent the endoscope from colliding with the nasal tissue and improve the safety of the surgical operation. Thereafter, robot-assisted endoscopic  
Figure 17: Endoscopic image during the interactive endoscopic nasal examination (sort by time).  
nasal examination experiment was performed using a high-imitation head model, and the results showed that the proposed human-robot cooperative control method based on VF can effectively realize the motion guidance and constraint of the robot, and help to improve the accuracy and safety of operation during endoscopic sinus surgery. Considering clinical applicability, the project team is now working on clinical experiments to further optimize the robot system.  
Conceptualization, Y.H. ([PERSON]) and J.W.Z.; methodology, Y.H. ([PERSON]), P.Z. and [PERSON]. ([PERSON]); experiments, [PERSON] ([PERSON]), P.Z., B.L.Z., and X.Z.Q.; writing--original draft preparation, [PERSON] ([PERSON]), and P.Z.; writing--review and editing, B.L.Z., X.Z.Q. and [PERSON]. ([PERSON]); project administration, [PERSON] ([PERSON]) and J.W.Z.  
This research was funded by the National Natural Science Foundation of China (Grant No. 61603374, U1813213 and U1713218), Shenzhen Fundamental Research Funds (Grant Nos. JCYJ20160608153218487 and JCYJ20180507182415428), Shenzhen Peacock Plan (Grant No. KQTD2016113010571019) and Shenzhen Key Laboratory Project (Grant No. ZDSYS201707271637577).  
The authors declare no conflict of interest.