# Fuzzy Echo State Network-Based Fault Diagnosis of Remote-Controlled Robotic Arms
## 1 Introduction  
In recent years, remote-controlled robotic arms have been widely used in industrial production, hazardous environment detection, medical surgery, and other fields [1, 2, 3]. It can replace manual labor to complete complex and dangerous operation tasks, which greatly improves work efficiency and safety. However, due to the complexity and variability of the teleoperation environment [4, 5], the high degree of coupling and the nonlinearity of the robotic arm system [6], and the long history of continuous work, the teleoperated robotic arm has a high incidence of failures in actual operation [7], which seriously affects its reliability and work performance. The reliability of the remote-controlled robotic arm system depends on the performance of each robotic arm and its communication quality [8]. Failure of a single arm can degrade the performance of its neighboring arms through communication, thus threatening the whole arm system [9]. Therefore, there is an urgent need for a method that can detect and diagnose abnormalities in teleoperated robotic arm systems at the initial stage of failure. Efficient and accurate fault diagnosis techniques [10] can not only buy valuable time for fault handling but also significantly reduce the system maintenance cost [11], reduce the risk of serious accidents leading to the paralysis of the whole system [12], and thus effectively guarantee the stable operation of the system and improve its reliability [13]. In this paper, we follow the terminology and methodologies outlined by [PERSON] and [PERSON] in their seminal work on model-based fault detection and diagnosis [14]. Most existing fault diagnosis methods for leader-follower robotic systems are based on analytical or observer-based models. These model-based approaches are known for their high accuracy and real-time performance under ideal conditions. For example, [PERSON] et al. [15] proposed a distributed fault detection and isolation scheme using sliding-mode observers to estimate system states based on both local and neighboring agent information. [PERSON] et al. [16] developed a fault diagnosis and fault-tolerant control strategy for multiple manipulators, which combined a learning observer with a radial basis function (RBF) neural network to approximate disturbances. [PERSON] et al. [17] introduced a robust distributed detection and isolation method leveraging Linear Matrix Inequality (LMI) techniques, while [PERSON] et al. [18] applied distributed PID control and observer-based techniques for fault detection within the context of multi-agent formation control. However, despite their effectiveness, model-based methods depend heavily on the availability of accurate system models, which can be difficult to construct for complex, nonlinear, or dynamically changing systems [19]. These methods are often sensitive to model uncertainties and external disturbances, which can compromise their robustness and generalization capability [20]. Furthermore, the design and tuning of such systems typically require extensive expert knowledge and manual adjustment [21], making them less efficient and more difficult to adapt to unseen or evolving fault conditions. In contrast, data-driven approaches, particularly those using deep learning, have emerged as powerful alternatives for fault diagnosis tasks [22; 23]. These methods can automatically learn features from raw sensor data, model complex nonlinear relationships, and generalize well across a variety of operating scenarios. By eliminating the need for explicit modeling and manual feature extraction, deep learning techniques improve robustness, scalability, and adaptability, making them especially suitable for remote-controlled robotic arm systems where uncertainty and real-time requirements are prevalent. Techniques such as the convolutional neural network (CNN) and recurrent neural network (RNN) have been successfully applied to various fault diagnosis tasks. [PERSON] et al.