# Adaptive Fuzzy-Based Fault-Tolerant Control of a Continuum Robotic System for Maximly Sinus Surgery
## 1 Introduction
This technique is divided into three main categories: (a) model-based algorithms, (b) knowledge-based techniques, and (c) hybrid-based fault-tolerant control methods [32]. Model-based and knowledge-based fault-tolerant control techniques have various positive points, but these techniques face a large challenge in the unlimited level of a faulty signal [18; 32]. Hybrid techniques for fault-tolerant algorithms are used to address this issue [33]. The feedback linearization algorithm can be a good candidate for a fault-tolerant control algorithm, but it must be robust. To improve robustness, the proposed observation-based feedback linearization controller is the best candidate. To increase accuracy, performance, and reliability, an adaptive, fuzzy observation-based feedback linearization fault-tolerant control algorithm is suitable for manipulators for a surgical robot for the sinus. Figure 2 shows the block diagram of the proposed algorithm for fault detection, estimation, identification, and fault-tolerant control. The proposed adaptive ARX-Laguerre T-S fuzzy robust feedback linearization observer has the following steps: (1) modeling the surgical robot for the sinus based on the ARX method; (2) modifying the performance of the ARX technique based on an orthonormal function and designing the ARX-Laguerre method; (3) improving the accuracy of the ARX-Laguerre technique based on the fuzzy logic algorithm and designing a fuzzy ARX-Laguerre system model; (4) designing a high-performance nonlinear observer based on the fuzzy ARX-Laguerre feedback linearization observation technique; (5) improving the robustness of the fuzzy ARX-Laguerre feedback linearization observer based on the variable structure algorithm; (6) improving the performance of  
faulty signal estimation based on the T-S fuzzy algorithm and designing a fuzzy ARX-Laguerre T-S fuzzy robust feedback linearization observer; (7) creating a residual generation and a threshold process for fault detection and identification; (8) detecting, estimating, and identifying faults; (9) reducing the fault effect in the surgical robot for the sinus based on a feedback linearization algorithm and improving the accuracy of the fault-tolerant control using the proposed observation algorithm; and (10) tuning the feedback linearization coefficients in the various conditions and online tuning for increasing the reliability and accuracy in the proposed observation-based feedback linearization fault-tolerant control using an adaptive method. This paper introduces three different problems and the solutions to solve these problems. Figure 2: The proposed algorithm for fault detection, estimation, identification, and tolerant control of a maxillary sinus continuum robot surgery. **Problem 1**. : _The main idea of the fuzzy observation-based technique for fault detection, estimation, and isolation is system modeling. Which types of system modeling are represented in this paper?_  
**Solution 1**. : _In the first step, the ARX technique is introduced to system modeling. To improve the robustness and reduce the effect of the noise, the Laguerre technique is used in the ARX technique as a ARX-Laguerre method. To reduce error of system estimation, a fuzzy ARX-Laguerre technique is performed for modeling of robotic maxillary sinus surgery (Section 2.2)._  
**Problem 2**. : _Another contribution of this paper is the design of robust and reliable technique for fault detection, estimation, and isolation. Which techniques are used in this paper?_  
**Solution 2**. : _In this study, a feedback linearization observer is used for fault estimation. To improve the robustness of the feedback linearization observer, a variable structure algorithm is employed in the next step. To modify the fault estimation accuracy in the robust feedback linearization observer, the fuzzy technique is presented in the third step (Section 3.1). To improve the fault detection and isolation, robust residual signal and threshold value are generated, compared, and classified (Section 3.2)._  
**Problem 3**.