# Fault-Tolerant Control of Multi-Joint Robot Based on Fractional-Order Sliding Mode
## 1 Introduction  
The robot is an important achievement produced by the comprehensive development of information science, artificial intelligence science, and modern processing and manufacturing technologies in the field of automatic control [1, 2]. It is widely used in various industrial fields, such as aerospace and industrial automation, and it is the object of key development and research in countries around the world. When the robot system fails, it is extremely important to design a fault-tolerant control law to ensure that the robot can perform basic control functions. Because of the complex structure and powerful functions of multi-joint robots, it is very difficult to achieve fault-tolerant control [3]. The fault-tolerant control of the robot is also divided into passive and active fault-tolerant control from the macroscopic level. The difference between the two is whether the controller is adjusted when the fault occurs [4]. For a passive fault-tolerant control system, the robust controller is designed mainly based on some prior knowledge of faults in the current system. Once the controller is designed, it will not be adjusted in real time. Active fault-tolerant control strategies may involve switching between multiple sets of control algorithms when a system fault occurs or correcting the gain of the controller according to the fault information. Considering the complexity of the multi-joint robot control system and the variety of fault types, there are few studies on the fault control of multi-joint robots using passive fault-tolerant control, and most of the existing literature uses active fault-tolerant control methods. In terms of active fault-tolerant control of the multi-joint robot, the existing research methods can be divided into three categories, and they are data-based, redundant sensor-based, and model-based fault-tolerant control methods [5]. The data-based fault-tolerant control method does not rely on an accurate robot system model and realizes fault tolerance by utilizing a large amount of online data in the process [6]. As the structure of the industrial robots gradually becomes more complex, the amount of data generated by the system gradually becomes larger, so more important parameters need to be fed back, which adversely affects the design of the controller. Therefore, the fault-tolerant control method based on pattern recognition is proposed. Under the premise that it is impossible to establish an accurate mathematical model of a multi-joint robot, the pattern recognition method is used to control the robot's fault tolerance, and the typical representative is deep learning. [PERSON] [7] developed a new model predictive control (MPC) method based on visual servos. In the presence of both kinematic and dynamic constraints, quadratic programming (QP) is used for control design, and neural dynamic optimization techniques are used to guide a wheeled mobile robot to move toward the desired target in a polar coordinate system. [PERSON] [8] proposed an enhanced robot skill-learning system that considers both motion generation and trajectory tracking. It combines the Gaussian mixture model and Gaussian mixture regression to improve the learning performance of the model. [PERSON] [9] used the improved neural network for the position error accumulation and convex constraint problems in the existing manipulator recurrent neural network controller design, and proved the effectiveness in the position regulation and tracking control of a robot. There are still many studies on using neural network methods to realize fault-tolerant control of multi-joint robots [10; 11; 12]. However, the neural network method needs to use the data set to train the model in advance. [PERSON] [13] assumes that the dynamic function of the robot is unknown, and proposes two dual adaptive neural network control schemes. The parameters of the neural network controller are estimated randomly in real time.