# Trajectory Planning of Robotic Arm Based on Particle Swarm Optimization Algorithm
## 1 Introduction  
The motion control of industrial manipulators typically involves a planning layer and a control layer. The former mainly focuses on understanding the relationship between the manipulator's position, speed, and time to realize the operation. Meanwhile, the control layer addresses how to ensure the actuator effectively follows the planned trajectory. Therefore, trajectory planning consists of basic research in the field of manipulator control. This has an important impact on the working efficiency, motion stability, and energy consumption of the manipulator [1]. Optimal trajectory planning aims to devise the optimal trajectory through task points, considering the predefined execution task points and motion constraints. The general trajectory planning algorithm transforms the original path into an optimized trajectory by planning parameters, such as the position, velocity, and acceleration for each task point on the manipulator's operational path. This enhances the accuracy and stability of the manipulator's trajectory [2]. Therefore, the purpose of this paper is to control the speed and acceleration of the manipulator during operation, aiming to enhance stability and reduce the impact and wear of the manipulator. In recent years, trajectory planning of industrial manipulators has been considered an important research focus in the field of robot control. Moreover, the research for a manipulator's optimal path planning has also seen important progress. In more detail, interpolation algorithms consist of a common method in manipulator trajectory planning due to their advantages, including simple calculation and easy implementation [3; 4; 5]. For instance, [PERSON] et al. [6] utilized an interpolation algorithm grounded in the forward-looking function to fine-tune the feed speed. This was achieved by predicting the future change in trajectory curvature. This approach not only ensured the precision of the interpolation algorithm but also enhanced processing efficiency. Moreover, [PERSON] et al. [7] considered the use of a Lagrange interpolation function as the trajectory function for individual joints to optimize the energy consumption of an industrial manipulator and derive the optimal trajectory. In addition, [PERSON] et al. [8] used multiquadric radial basic functions to generatethe manipulator's motion trajectory through the minimization of the acceleration integral and the consideration of the boundary conditions and the kinematic limits. Compared to other methods, this algorithm has higher smoothness. However, its accuracy is affected by the number of interpolation functions and interpolation nodes; consequently, it may not be effective when dealing with complex trajectory curves. Moreover, the swarm intelligent control algorithm is a heuristic algorithm developed to solve the motion path of a manipulator through the simulation of the swarm intelligent behavior in nature. This latter is characterized by its strong adaptability and ability to handle complex motion trajectory, including the genetic algorithm (GA) [9; 10; 11], the artificial immune algorithm [12], and the particle swarm optimization (PSO) algorithm [13; 14]. The core idea of the PSO algorithm consists of finding the optimal solution of the problem by simulating the flock predation process and constantly adjusting the speed and position of the particles [15]. Compared to other similar algorithms, PSO has high efficiency, global optimization ability, adaptability, and expansibility. However, the traditional PSO algorithm is prone to premature convergence. Therefore, several researchers have improved the algorithm's performance by adjusting relevant parameters and combining them with other intelligent algorithms. For instance, [PERSON] et al. [16] proposed an improved PSO algorithm combining the fuzzy reward and punishment theory to resolve the manipulator's trajectory planning problem when having multiple Degrees of Freedom (DoF).