# Adaptive Fuzzy-Based Fault-Tolerant Control of a Continuum Robotic System for Maximly Sinus Surgery
## 1 Introduction
Hybrid fault detection, estimation, and identification algorithms are used to design a stable and reliable technique by employing multiple methods. Different techniques have been used for hybrid methods [18, 19, 20]. In this study, the hybrid method is designed based on three different algorithms: (a) signal-based method, (b) model-reference technique, and (c) knowledge-based algorithm. Signal-based and knowledge-based methods are used for system (surgical robotic system for the sinus) modeling based on torque and pose (position and orientation) data. A model reference technique is used to design a robust feedback linearization observer based on the variable structure technique for fault detection, estimation, and identification. A knowledge-based algorithm is used to design a Takagi-Sugeno (T-S) fuzzy technique to improve the fault estimation accuracy in the fuzzy autoregressive with exogenous input (ARX)  
Figure 1: Maximly sinus position: (**a**) front view and (**b**) left view. Laguerre robust feedback linearization observer. The hybrid technique based on adaptive fuzzy observation-based estimation and feedback linearization control is used for fault-tolerant control. Physical-based system modeling and signal-based methods for system estimation are the main methods used for modeling complex systems such as surgical robots for the sinus. Apart from the reliability of physical-based modeling of a surgical robot for the sinus, this technique has drawbacks in highly uncertain (faulty) conditions. System estimation and identification techniques such as ARX, autoregressive moving average with external input (ARMAX), orthonormal function bases (OFB), and generalized orthonormal bases (GOB) methods have been used for system estimation in various systems. Independence of the system time delay and reduction of the number of parameters are the main advantages of orthonormal techniques such as OFB and GOB with respect to classical system modeling such as ARX and ARMAX techniques. Apart from the advantages of orthonormal techniques compared to classical algorithms, these techniques have two difficulties, calculating the optimal orthonormal values and the number of restrictions in decoupled systems. To address these issues, the ARX-Laguerre technique was presented in a number of reports [21; 22; 23]. In real world applications, the impact of noise plays a significant role in accurate system estimation. To circumvent these challenges, the fuzzy ARX-Laguerre technique is presented in this research. Linear-based observation techniques and nonlinear-based observation algorithms are the main techniques used to design observation systems [22; 23; 24; 25]. Linear observation systems such as proportional integral (PI) controllers have been applied in several systems for control and fault diagnosis, but their effectiveness in the presence of uncertainties is the main restriction of these algorithms [26]. To circumvent this restriction, nonlinear-based observation techniques such as variable structure techniques [22; 27], feedback linearization methods [26], and fuzzy algorithms have been recommended [28; 29; 30]. Despite the advantages of nonlinear observers, a feedback linearization observer has the challenge of limited robustness [26], a variable structure observer has the limitation of chattering in uncertain conditions [22], and fuzzy logic observers have the challenge of reliability and predefinition of fuzzy gain updating factors [31] for fault detection, estimation, and identification. Consequently, a hybrid algorithm is suitable for fault detection, fault estimation, and fault identification for a surgical robot for the sinus. Linear- and nonlinear-based fault-tolerant control techniques are the main algorithms for reducing or eliminating the effects of faults in a surgical robot for the sinus. Linear-based fault-tolerant control techniques have two main drawbacks: (a) coupling effects and (b) increase in gear ratio [32]. However, several techniques have been introduced as nonlinear-based fault-tolerant algorithms.