# Adaptive Fuzzy-Based Fault-Tolerant Control of a Continuum Robotic System for Maximly Sinus Surgery
## 1 Introduction  
The maxillary sinus is a conic, hollow space in the bones of the face that connects to the nose. It is the largest cavity of air in the body, and its main function is mucus production. The maxillary sinus can experience many health issues, such as nasal polyps, maxillary sinusitis, and nasal sinus cysts, which can cause infections [1, 2]. Task complexities, narrow geometry, and limited accessibility to the sinus creates several challenges for maxillary sinus surgery. Infection of a maxillary sinus causes pain and pressure (e.g., headache and toothache). Therefore, finding a good method for maxillary sinus surgery is important [3]. These techniques are divided into two main groups: (a) minimally invasive surgery, and (b) a non-invasive surgery technique. The creating an incision in the face, pain, and long recovery time are main challenges of the open sinus surgery. In most of cases, sinus surgery is performed as minimally invasive surgery [4]. The natural orifice transluminal endoscopic surgery (NOTES) is one of the important techniques for minimally invasive surgery. Despite the severaladvantages of NOTES, surgeons still have challenges due to the narrow operating space. To improve the performance of endoscopic surgery, a number of continuum robots (e.g., concentric tube robots, tendon-driven robots, and soft robots) have been represented [3,4]. While concentric tube robots have several advantages, limited bending angle and small stiffness are two drawbacks of the technique [5]. Various tendon-driven robots have been developed by various researchers for surgery [3,6]. A soft robot is a promising technique for surgical techniques. This technique has been used in various surgery but it is not useful for maxillary sinus surgery [3,7]. Figure 1 illustrates the position of the maxillary sinus. Robot-assisted surgery is used to reduce surgeon's hand tremors, postoperative complications, and pain and to increase the precision of the actions performed during surgery. Robots have been widely used in many medical fields such as orthopedics, neurology, urology, and cardiology. Robot-assisted surgery is expanding its effects in the general medical field but has various challenges, such as non-linear behavior, the need for high-accuracy control, insertion depth perception, contact force feedback, and fault diagnosis. Various defects in robotic assistants can be categorized as actuator faults, sensor faults, and system faults. The actuator fault is affecting the continuum robot inputs. The actuator fault can be caused by abnormal operation or material aging and can drastically change the system behavior and operation. Therefore, a fault in a continuum robot motor's joint or operator can cause the actuator fault. Continuum robots are usually equipped with sensors to recognize the surrounding environment. Unfortunately, sensors are susceptible to faults and they might lead to task failure. In this paper, actuator and sensor fault detection, diagnosis, and tolerant control are analyzed. To analyze the condition of actuator and sensor faults in robot-assisted surgery, various monitoring techniques for robot conditions such as torque, voltage, current, and vibration have been reported [8, 9, 10]. This research exploits torque measurements because these signals are suitable for system and fault modeling, identification, estimation, and fault-tolerant control. Various techniques have been presented recently for surgical robot fault detection, identification, and tolerant control and can be divided into two main categories: a) hardware-based techniques that rely on various physical instruments installed on the surgical robot and b) software-based techniques that utilize limited equipment. Different techniques are used for software-based fault detection, estimation, and identification, such as model-reference techniques [11,12], signal-based methods [13,14], knowledge-based algorithms [15, 16, 17], and hybrid methods [18, 19, 20].