# Human-Robot Cooperative Control Based on Virtual Fixture in Robot-Assisted Endoscopic Sinus Surgery
## 4 Experiments and Discussion
### Robot-Assisted Endoscopic Nasal Examination Experiment  
In endoscopic nasal examination surgery, the surgeon inserts the endoscope into the small, narrow nasal cavity and carefully examines the anatomy, such as the shape of the turbinate and the opening of the sinus. This surgery is a typical surgical procedure in nasal surgery, so it is selected in this experiment.  
**Experiment model.** Considering that a real human corpse head is very rare and an animal's nasal cavity is not similar to a human's cavity, a high-imitation head model with fine anatomical structure (Phacon Company, Germany) is adopted in this experiment, as shown in Figure 14.  
**Surgical path planning.** A three-dimensional model of the nasal cavity is obtained by reconstruction of the nasal CT image sequence, and then the surgical path from the entrance point of  
Figure 14: High-imitation head model with fine anatomical structure of the nasal sinus. (**a**) Nasal cavity module; (**b**) high-imitation head model.  
Figure 13: Comparison of the experimental results of the composite FRVF. (**a**) Endoscopic tip trajectory without FRVF constraint; (**b**) endoscopic tip trajectory with the composite FRVF constraint.  
the nasal cavity to the opening of each sinus (taking maxillary sinus as an example) is obtained by the surgical planning module.  
**Interactive endoscopic nasal examination.** The surgical scene of the interactive endoscopic nasal examination is shown in Figure 15. The upper left corner of the figure shows the real-time image of the endoscope during examination, and the upper right corner of the figure shows the control system interface and the virtual robot system.  
Based on the proposed human-robot cooperative control method, the operator drags the endoscope at the end of the robot and performs interactive nasal sinus examination, browsing along the planned path that is a GVF based on a spatial curve. During this process, the motion of the endoscope tip is constrained by the robot motion constraint model, and the operator constantly adjusts the pose of the endoscope to see the small and deep anatomy inside the nasal cavity from different angles of view. Figure 16 shows the endoscope tip trajectory together with the preoperative planned trajectory during interactive endoscopic nasal examination. It can be seen that due to the effect of the VF constraint, the trajectory of the endoscope tip is substantially coincident with the preoperative planned trajectory, and the maximum deviation is approximately 1.1 mm. Figure 17 shows the endoscopic image during the interactive endoscopic nasal examination. As shown in the figure, the endoscopic field of view is clear throughout the whole examination.  
Figure 16: The endoscope tip trajectory and the preoperative planned trajectory.  
Figure 15: Surgical scene of the interactive endoscopic nasal examination.  
Through the above experiment, it can be seen that the proposed human-robot cooperation control method based on VFs can effectively realize the motion guidance and constraint of the robot, improving the accuracy and safety of surgical operation during surgery.