## 1 Introduction  
As industrial automation continues to advance, robotic arms are increasingly deployed in a variety of work environments. However, due to the complexity and diversity of these environments, accurately establishing mathematical models for these robots remains a significant challenge [1]. Moreover, the control of multi-joint robotic arms' trajectory is a focal area of current technological research [2]. To effectively address these challenges, researchers have proposed various control strategies. These include the model reference controller, which utilizes a predefined model to adjust control parameters [3, 4]; the adaptive controller [5, 6, 7], capable of self-adjusting based on variations during operation [8]; the robust controller, designed to counteract operational deviations and external disturbances [9, 10, 11]; and the sliding mode controller (SMC) [12], which manages system uncertainties by switching control strategies [13]. Each of these methods uniquely contributes to enhancing the precision and reliability of robotic arm operations. The controlled robotic arm experiences numerous variations due to actual working conditions on-site. For instance, [11] proposes an alternative solution for the crimping process, which can enhance the precision of positioning movements and the stiffness of structural components in industrial applications [14]. However, the disadvantages of model predictive control (MPC) include its high computational complexity and stringent real-time requirements,as well as a strong dependence on the accuracy of the system model; the control performance may significantly deteriorate in the presence of model inaccuracies or noise. The drawbacks of adaptive controllers include high design complexity, the potential for system instability due to parameter adjustments, sensitivity to dynamic changes and external noise, and the need for significant computational resources in practical applications. Similarly, the disadvantages of robust control include a conservative design approach that may lead to suboptimal performance, the requirement for complex mathematical models, and difficulties in handling system nonlinearities and uncertainties in real-world applications. Given these limitations, alternative control strategies have been explored, among which sliding mode control (SMC) stands out for its robustness against system uncertainties and external disturbances. However, sliding mode control systems often experience oscillations, commonly known as chattering, primarily due to external disturbances and parameter uncertainties within the system. To mitigate this prevalent issue, researchers have extensively explored and developed a range of innovative improvement strategies, enhancing the robustness and reliability of these systems in dynamic environments. [PERSON], [PERSON], and [PERSON] designed a fuzzy double hidden layer recurrent neural network controller using an objective sliding-mode control (OSMC) which uses a combination of a fuzzy neural network and a radial basis function neural network to improve the accuracy of a nonlinear approximation [15]. [PERSON], [PERSON], and [PERSON] introduced a novel sliding mode control (DOB-PD-SMC) that integrates a disturbance observer with proportional-differential elements to enhance the precision of robot-assisted surgical training by effectively mitigating controller output jitter [16]. In [17], a dual sliding mode vector control approach effectively estimates the speed and position of a Permanent Magnet Linear Synchronous Motor (PMLSM), combining enhanced Sliding Mode Observer (SMO) with Generalized Fuzzy Output Integral Sliding Mode Control (GFOISMC) to significantly reduce jitter and boost robustness, as validated by simulation results. In [18], a sliding mode active disturbance rejection control (SMADRC) system for AC/DC converters is introduced, incorporating a linear extended state observer (LESO) and a disturbance compensator to effectively mitigate total system disturbances in the voltage outer loop.