# Fault-Tolerant Control of Multi-Joint Robot Based on Fractional-Order Sliding Mode
## 1 Introduction
The effectiveness of the controller in the trajectory tracking problem of a differentially driven wheeled mobile robot is verified using statistical hypothesis testing. The neural network model is used in the design process of the robot's fault-tolerant controller, which needs to be combined with a high-performance computer to achieve decent results. Therefore, the neural network model is not suitable for the control process with high dynamic performance requirements. The fault-tolerant control of the multi-joint robot based on additional sensors improves the stability of the robot control system by installing redundant sensors at the beginning of the design. Georgethuruthel T. [14] uses a combination of redundant and disjoint strain sensors to compensate for the time-varying hidden state of the system and achieves decent static variable estimates on pneumatic actuators. Professor [PERSON] of MIT has designed a class of small autonomous robot systems for outer space missions, equipped with more than sixty sensors, which brings challenges to the structural design of the system and reduces the payload of the robot [15]. Fault-tolerant control of robots based on additional sensors will increase the cost of the system and limit the development of robot miniaturization. At present, fault-tolerant control is realized by software signal processing, which has gradually become an alternative solution [16; 17]. The model-based fault-tolerant control law for a robot involves the mathematical model of the robot in the design process so that it can predict what effect the control output will have on the robot system and the system parameters can be tuned accordingly. The representative of these methods includes adaptive control, optimal control, model predictive and back-stepping control, etc. [18; 19; 20]. [PERSON] develops an adaptive compensation control scheme for two physically linked two-wheel-drive mobile robots with multiple actuator faults [21]. [PERSON] investigates the fully distributed observer-based adaptive fault-tolerant synchronization problem (SP) of multiagent systems with event-triggered control mechanisms [22]. [PERSON] proposed an adaptive fuzzy fault-tolerant tracking control for partially unknown systems with actuator faults [23]. The main disadvantage of adaptive control is that it is difficult to ensure the global stability of the closed-loop system in the whole adaptive process. The other popular control method is optimal control. [PERSON] used optimal planning and control schemes for real-world robotic applications [24]. [PERSON] researched a symplectic instantaneous optimal control for robot trajectory tracking [25]. Considering uncertainty in optimal robot control, [PERSON] studied the stochastic optimal control problem with high-order cost statistics, which promotes the application of robots [26]. The control law of optimal theory relies heavily on the model of robots, but it is not easy to obtain an accurate model of the robot, which limits the application of optimal control. There are many other types of research involving fault tolerance control of the robots. [PERSON] [27] used the equivalent replacement of the mass-spring-damper model for the space station robot astronauts, established a viscoelastic dynamic humanoid robot model in a microgravity environment, and initially proved its effectiveness. [PERSON] [28] combined MPC and adaptive control to study the trajectory tracking control problem of mobile robots and achieved good control results. Many other model-based multi-joint control schemes are introduced in [29; 30; 31]. The advantage of this type of control method is that the control effect is better and the performance can be optimized, while the disadvantage is that the mathematical model of the controlled object needs to be accurately established, and the control effect may be poor when the modelling is not accurate.