# Fault-Tolerant Control of Multi-Joint Robot Based on Fractional-Order Sliding Mode
## 2 Related Works  
So far, the fault-tolerant control of multi-joint collaborative robots is still divided into two types and they are model-free and model-based control law design methods, of which proportional-integral-derivative (PID) control and MPC still account for the majority. The above two methods are typical representatives of model-free and model-based fault-tolerant control laws, respectively. Generally, PID controller parameters are difficult to adjust, the parameter margin of the controller is difficult to obtain, and the dynamic process cannot be accurately controlled [32]. As for MPC, theoretically, there is still no clear explanation for the stability of closed-loop systems. Data-driven fault-tolerant control has become a research hotspot in recent years, but the computational complexity and the application cost of this method are much higher than those of other methods. For the fault-tolerant control of multi-joint robots, advanced control algorithms still need to be studied. Sliding mode control has a strong application prospect in the fault-tolerant control of multi-joint collaborative robots because the design process of the control law is based on the controlled object model, but does not rely on it strongly [33; 34; 35]. [PERSON] [36] uses a fast non-singular terminal sliding mode controller for the fault-tolerant control of the manipulator's arm. The proposed controller can keep the integral non-singular fast terminal sliding mode control in high robustness, fast transient response, and finite time convergence advantages. However, its disadvantage is that the proposed non-singular fast terminal sliding mode control law design process relies on the prior knowledge of disturbance and uncertainty thresholds, for which it is necessary to use adaptive technology to estimate the upper limit of the disturbance. [PERSON] [37] studied the problem that the flexible actuators of flexible multi-joint collaborative robots cannot guarantee high tracking performance under the condition of mismatched interference using continuous sliding mode control, and it adopts the generalized proportional-integral observer technique and designs a new sliding surface based on the disturbance estimation to deal with the adverse effects of matching/mismatching time-varying disturbances. There are still many studies on the control of multi-joint collaborative robots using conventional low-order sliding modes. As the sliding surface of the low-order sliding mode design is linear, the performance is difficult to guarantee [33; 34]. The design of a high-order sliding mode controller gradually enters the field of robot fault-tolerant control [36; 38]. Although the high-order sliding mode can make the control input continuous, it avoids the occurrence of high gain switching, so that the chattering phenomenon of the low-order sliding mode control can be suppressed. However, the high-order sliding mode also has shortcomings. For example, it requires the prediction of the upper bound of the uncertainty of the robot system. There are still many difficulties in the parameter selection of the high-order sliding mode [39]. Considering the drawbacks of the existing SMC applied to robot control under actuator fault, in this paper, the FSMC is proposed and well designed. The main innovations are summarized as follows, compared with common regular SMC. (1) The fractional differential operator is introduced into the sliding mode surface design process. From the perspective of the complex frequency domain, the differential operator has the advantage of phase lead; thus, the response time is reduced. The realization of the differentiation operation involves summation, so the ripples in the output voltage of the controller are eliminated. (2) The FSMC controller is designed and its robustness and stability are guaranteed by the Lyapunov function, so the controller can handle a variety of serious conditions, such as actuator constant gain fault and constant deviation fault. This can be seen in the experiment section.