# Human-Robot Cooperative Control Based on Virtual Fixture in Robot-Assisted Endoscopic Sinus Surgery
###### Abstract
Considering that the end-effector of the multi-arm form robot is generally large in size, it can only be applied to the types of surgery that have a large operation space, such as abdominal cavity surgery, and it cannot be applied to types of surgery with a small operation space, such as the nasal cavity. For the active control mode based on the voice and head movement, the human-robot interaction efficiency is low, and the training time is long, which requires further research. For robot-assisted endoscopic sinus surgery, due to the narrow and complex anatomy of the nasal cavity, the endoscope easily collides and interferes with the nasal tissue. To ensure the safety of the operation, it is necessary to restrain the movement of the endoscope at the end of the robot. Presently, there are two main motion constraint methods for robots: Hardware constraint based on robot structure design and software constraint based on algorithms. Hardware-based constraint is generally considered to be more safe, but often less flexible, such as RCM (remote center of motion) constraint. VF (virtual fixture) represents one of the most important software-based constraints, which was proposed by Professor [PERSON] [26, 27] in 1993. VF is a constraint method that uses an algorithm to generate invisible spatial motion constraint, thereby limiting robot motion. Current VF can be divided into GVF (guiding virtual fixture) and FRVF (forbidden regions virtual fixture) [28]. A GVF is generally used to guide the end-effector of the robot to move along a predefined trajectory to avoid interference; an FRVF is generally used to prevent the end-effector of the robot from entering a specific area and can be used to protect critical tissues and organs during surgery. [PERSON] et al. [29] prevented the robot end-effector from entering a specific area by constructing a VF \"virtual wall\" in robot-assisted cardiac surgery and verified the effectiveness of the VF through simulation. [PERSON] et al. [30] proposed a VF library design method by introducing VF into the virtual reality system. [PERSON] et al. [31] proposed a dynamic VF design method for minimally invasive cardiac surgery, in which the interpolation algorithm was used to calculate the dynamic VF at different moments in the heartbeat cycle to avoid the probe entering the dangerous area during operation. [PERSON] et al. [32] restricted the movement of the end-effector of a spinal surgical robot by introducing a GVF (straight type) and an FRVF (cone type) to improve the safety of the operation. [PERSON] et al. [33, 34, 35] used an optimization constraint algorithm to generate VFs to solve the problem of a narrow operating space in endoscopic sinus surgery, but the algorithm is too complicated and does not consider nasal soft tissue. In summary, the existing VF research is mainly based on regular geometric shapes. Due to the complex and narrow anatomical structure of the human nasal cavity, the use of regular geometric shapes as a motion constraint will result in the loss of substantial valuable operation space, which is not allowed in the surgical operation. Therefore, it is urgent that the problem regarding how to properly fit the VF model with a 3D anatomical structure of the human nasal cavity is solved and the safety constraint of the nasal endoscope's movement is realized. Based on the above control mode and safety constraint analysis, considering the current clinical requirements of endoscopic sinus surgery, this paper proposes a human-robot cooperative control method based on VFs in robot-assisted endoscopic sinus surgery. This method uses admittance-based cooperative control to realize human-robot interaction between the surgeon and robot during surgery; the VFs are used to restrain and guide the movement of the robot, thereby ensuring the movement safety of the nasal endoscope.