## 1 Introduction  
The development of robotic arms has seen significant advancements [1; 2; 3], driven by widespread application in various fields such as manufacturing, medical robotics [2], and aerospace [3]. Robotic arms are integral to operations that require precision and dexterity. However, the inherent flexibility of these systems poses challenges, particularly as regards minimizing tracking errors and suppressing vibrations, exercises which are crucial for maintaining the desired performance and longevity of a system [1; 4; 5; 6]. For example, precise path control is vital for the use of multi-DOF robotic arms in aerospace, while in manufacturing faster responses and greater stability can enhance production efficiency. In existing research, numerous control methods for robotic arms have been explored, including classical PID control, the assumed mode method (AMM) for multi-degree-of-freedom flexible robotic arms, and adaptive robust control [7; 8; 9; 10; 11; 12; 13]. These methods often struggle to balance rapid error reduction with minimal overshoot and stable transient response, leading to performance trade-offs [14; 15; 16; 17; 18; 19]. Furthermore, current strategies frequently encounter issues related to input saturation and system uncertainties, further complicating the design and implementation of control mechanisms. Additionally, traditional methods often struggle with the trade-off between fast convergence and vibration suppression. Therefore, the improvement of tracking accuracy and control performance has emerged as a key research focus [2; 3]. To address these challenges, we propose an improved sparrow search algorithm (ISSA), which incorporates four significant enhancements to optimize control parameters more effectively. In the process of controlling robotic arms, it is known that rapid convergence, when dealing with input nonlinearities, can sometimes increase the amplitude of vibrations, thereby making it challenging to achieve both good error convergence and vibration suppression simultaneously. Fixed-time control methods offer an effective solution for attaining high precision and rapid convergence [14; 15; 16; 17]. A major advantage of this control approach is that the setting time is independent of initial conditions and is solely determined by the controller gains. Furthermore, the extensive research on fixed-time control provides valuable references for further exploring its capabilities and applications [18; 19; 20; 21; 22; 23; 24]. The performance of robotic arm control is reflected in the selection of controller gains. When the control gain is too high, the error converges quickly but this is accompanied by oscillations in the output torque. When the control gain is too low, the error converges more slowly, but the output torque is relatively smooth. To solve this problem, we introduce an improved seagull search algorithm to find the appropriate controller gains, ensuring that the tracking error converges to within a small set of values while maintaining a fast convergence rate and relatively stable output torque. The sparrow search algorithm (SSA) provides an effective global optimization solution for the parameter optimization of robotic control systems by simulating the social behavior and foraging strategies of sparrows. This algorithm is particularly suitable for dynamic environments, where it automatically adjusts control gains to enhance the performance and adaptability of robots [25]. The improved seagull search algorithm includes four key enhancements. Firstly, the ISSA uses good point-to-set mapping to initialize the population, ensuring that there is a well-distributed set of initial solutions that enhances the diversity of the search space [26]. Secondly, the proportion coefficient is adaptively improved, balancing exploration and exploitation to maintain search efficiency throughout the optimization process [27; 28]. Thirdly, the explorer's position update formula is refined to enhance global search capabilities and prevent premature convergence [25].