# Review of Fault-Tolerant Control Systems Used in Robotic Manipulators
## 2 Artificial Intelligence Methods in FTCS
The inference block receiving the data provided information about the axis that was damaged. The algorithm was successfully tested on a simulation of the ER5u robot in a MATLAB environment. The authors of [24] presented a system in which an artificial neural network in the form of a multilayer perceptron (MLP) was responsible for monitoring and fault detection (FD). This system consisted of a block in which the MLP provided information about the system failure while the fuzzy logic rule base made decisions about the type of fault and its location. The authors demonstrated the performance of fault detection based on a neuro-fuzzy (NF) application for a robotic arm with 5 degrees of freedom when one of the robot's axes fails. The architecture of the system was similar to the solution described in [23] but in this solution, the inference by the fuzzy logic system was based on the output of the neural network. The authors of [25] proposed a new solution in the form of self-tuning fuzzy proportional-integral-derivative non-singular fast terminal sliding-mode control (SFT-PID-NFTSM) with time delay estimation (TDE). The proposed method involved the self-tuning of the  
Figure 1: AFT2 BC control scheme [17], where \(u\) are the desired robot axes’ positions. proportional-integral-derivative (PID) block of the controller using fuzzy logic algorithms. Compared to other well-known methods described in the literature, such as the PID controller or the controller with a fuzzy logic block responsible for the self-tuning of the PID block, i.e., (PID-NFFSM), the results of [25] showed that the controller proposed in this work was more stable, had less overshoot, and improved transient responses. In addition, the integration of TDE reduced the required computational power of the controller and also helped to eliminate the requirement to know the exact dynamics of the system. The architecture of this system is shown in Figure 2. In order to fully understand the operation of the presented architecture, it is necessary to explain Formulas (7)-(15), which underpin the system [25]:  
\[s=e+k_{1}e^{[\lambda]}+k_{2}e^{[\frac{p}{q}]}, \tag{7}\]  
where s is the NFFSM sliding surface, e is the error, \(k_{1}=diag(k_{11},k_{12},\ldots,k_{1n})\in R^{nxn}\) and \(k_{2}=diag(k_{21},k_{22},\ldots,k_{2n})\in R^{nxn}\) are two positive definite matrices, \(p\) and \(q\) are two positive odd numbers selected to satisfy the conditions \(1<\frac{p}{q}<2\)_and_\(\lambda>p/q\),  
\[S_{PID}(t)=K_{p}s(t)+K_{i}\int_{0}^{t}s(t)dt+K_{d}\frac{ds(t)}{dt}, \tag{8}\]  
where \(S_{PID}\) is the sliding surface based on PID-NFFSM, \(K_{p}\), \(K_{i}\), \(K_{d}\) are the proportional, integral, and derivative gains,  
\[u_{a}=W^{T}(e_{1}\dot{e}_{1})\Theta, \tag{2}\]0  
where \(x_{1}=q,x_{2}=\hat{q},u=\tau\) are the state variables, \(\tau_{d}\) is the disturbance torque, \(\Delta_{0}\) is a constant, \(\Delta(x_{1},x_{2},u,\tau_{d})\) covers all the effects of the uncertainties, disturbances, and faults,  
\[u_{a}=W^{T}(e_{1}\dot{e}_{1})\Theta, \tag{2}\]1  
where \(\Delta_{0}\) is a constant,  
\[u_{a}=W^{T}(e_{1}\dot{e}_{1})\Theta, \tag{2}\]2  
where \(\wedge(\hat{e},\Delta)_{(t)}\) is the unknown function,The authors of [26] presented a new method of fault diagnosis and fault-tolerant control for a manipulator using a combination of a support vector machine (SVM)-based neural adaptive high-order variable structure observer (ANHWSO) and an adaptive modern fuzzy backstepping variable structure controller (AMFBVSC). The architecture of this control system is shown in \[u_{a}=W^{T}(e_{1}\dot{e}_{1})\Theta, \tag{2}\]3 An SVM machine learning technique was used in this method for error detection and identification and the control process was based on AMFBVSC. The proposed control method, i.e., ANHVSO, improved the performance of fault identification significantly compared to the neural high-order variable, structure observer (NHVSO), and variable structure observer VSO.