# Adaptive Fuzzy Command Filtered Tracking Control for Flexible Robotic Arm with Input Dead-Zone
## 1 Introduction  
Flexible robotic arms are gaining prominence in various fields, such as the manufacturing industry, the medical sector, and food processing. As a pivotal branch of robotics technology, they offer exceptional control precision, response speed, and load capacity [1, 2]. In the pursuit of enhanced flexibility, precise adaptability, and heightened safety, flexible robotic arms are emerging as substitutes for rigid counterparts. Their distinctive design and material characteristics reveal significant potential, making them a preferred choice. They not only inherit the advantages of traditional robotic arms, such as outstanding control performance and high load-bearing capacity, but also excel in terms of their adaptability and multifunctionality. Their pliable structures and elastic properties enable them to effortlessly handle various workpieces with complex shapes, even within confined and hazardous environments. This flexibility allows them to overcome the limitations of traditional robotic arms in these scenarios [3, 4]. However, it is important to note that flexible robotic arms also face certain challenges. Their flexible structures and complex motion characteristics introduce complexities such as nonlinearity, strong coupling, and temporal variations. Additionally, uncertainties in parameters, load disturbances, input saturation, and other issues significantly impact the accuracy and stability of the system. Addressing these factors and achieving higher levels of accuracy in control effectiveness remain pressing challenges that need to be resolved [5, 6]. In this context, this paper aims to investigate the control challenges faced by flexible robotic arms when encountering these issues. In this paper, we will introduce an innovative control approach that combines techniques such as adaptive control, fuzzy control, and observer design to achieve trajectory tracking control for flexible robotic arms. Additionally, we will also discuss how to address common dead-zone input problems in flexible robotic arm systems and how to handle systems with unknown parameters. Through this researchstudy, we aim to provide valuable insights for addressing the complex challenges in the control of flexible robotic arms and inspire future research directions. In recent years, the control issues related to flexible robotic arms have garnered significant attention from both domestic scholars and scholars from elsewhere. To date, numerous effective control methods have been developed, including adaptive control [7; 8], robust control [9; 10], and sliding mode control [11], among others. For strictly feedback-form nonlinear systems, the backstepping design method is considered one of the most effective control approaches [12]. However, backstepping can only be applied to control systems with precisely known dynamics. In practical engineering, uncertainties and nonlinearities are commonly present, making it challenging to obtain precise mathematical models for these systems. Therefore, methods like adaptive fuzzy control [13] and neural network control [14], which do not rely on exact mathematical models, are better suited for designing controllers for unknown nonlinear systems. Combining these methods with backstepping has resulted in numerous research achievements. Furthermore, with the advancements in adaptive fuzzy control and backstepping design techniques, the backstepping method [15] has been extensively used to address control problems in uncertain nonlinear feedback systems. While the proposed adaptive control methods ensure control system stability and favorable control performance, traditional backstepping approaches face issues of computational explosion during controller construction due to the repeated differentiation of virtual control variables [16; 17]. To address these problems, researchers have proposed dynamic surface control techniques [18; 19; 20]. These techniques introduce first-order filters in the process of backstepping recursion to handle computational complexity.