# Implementation of Fault-Tolerant Control for
## 1 Introduction
[21] proposed cross-coupling control for mobile robots. He suggested that minimization of the most significant error leads to coordination of the motion of the two wheels. [PERSON] et al. [22] introduced synchronization errors, a new type of cross-coupling error, in controlling a parallel robot manipulator. Synchronization control has also been applied in multi-robot cooperation [23; 24]. Synchronization techniques combined with the sliding mode method have attracted the interest of many researchers. The position and velocity synchronization error have been used instead of position and velocity error, respectively, in sliding mode control structures [25]. [PERSON] et al. [26] also proposed a robust synchronous control based on a sliding mode variable structure for multi-motors. These studies [23; 24; 25; 26] have applied synchronization control techniques to a parallel robot, multi-robot cooperation, and multi-motors to improve trajectory tracking performance. This work is interested in addressing a slow response issue by using the synchronization control technique, which can make the position error at each joint equal. Therefore, the system can quickly respond to a fault due to the constraint of synchronization control before the controller has the feedback information from the fault estimation process. Considering the dynamic coupling effects between actuators and the upper bound of the uncertainties, the effectiveness of synchronization techniques might be somewhat limited to improvements of the trajectory tracking control. However, synchronization techniques become more effective in critical conditions, which lead to applying synchronization techniques to the fault-tolerant control. The contributions of this paper are summarized as follows:  
1. Synchronization techniques are applied to fault-tolerant control for robot manipulators for the first time. Compared to active fault-tolerant control using conventional sliding mode control, the proposed system has achieved higher accuracy, robustness, and faster system reconfiguration when faults occur. These results confirm that synchronization techniques are very effective in fault-tolerant control. 2. The stability of the proposed AFTC with the synchronous sliding mode technique is demonstrated using analysis via Lyapunov theory. Based on the extended state observer, the proposed controller can easily monitor faults without detection and isolation processes. This feature is helpful in maintenance systems as well as maintenance planning systems. 4. The experimental results show that the proposed control can be easily applied to a real system with robust performance. In this paper, we present a fault-tolerant control for robot manipulators based on synchronous sliding mode control. Section 2 describes the robot dynamic models. Section 3 explains the process of fault estimation with the extended state observer for robot manipulators. In Section 4, a fault-tolerant control based on synchronous sliding mode control is presented and its stability is demonstrated. In Section 5, a simulation study of the proposed fault-tolerant control for a 3-DOF manipulator was conducted to show the method's effectiveness. In Section 6, real implementation of the FTC for a 3-DOF FARA AT2 robot was carried out in two cases: a single fault and multiple faults. Finally, conclusions are discussed in Section 7.