# Analysis and Simulation of Polishing Robot Operation Trajectory Planning
## 1 Introduction  
With the development of modern science and technology, robots are widely used in various production industries, which greatly improves the efficiency of industrial production. In the realm of manufacturing, the precision and efficiency of grinding robots are largely contingent upon the optimization of their trajectory planning. The core scientific problem addressed in this study is the optimization of trajectory planning to enhance both the precision and energy efficiency of robotic grinding operations. Trajectory planning is a pivotal aspect of robot motion control, encompassing the generation and optimization of motion paths for the robot's end-effector (e.g., a grinding tool) to facilitate efficient and precise grinding operations. This involves addressing the scientific challenge of optimizing both the accuracy and the energy consumption of the robotic operations. The quality of trajectory planning affects the movement effect of the robot and then affects the quality of grinding. Trajectory planning is the prerequisite for achieving optimal performance in grinding robots. Linear and arc trajectory planning are two basic trajectory planning methods. Because the planned trajectory is relatively simple, the application surface is narrow. Traditional trajectory planning techniques have many drawbacks, such as not finding a global solution, requiring gradients, not being used for discontinuous functions, etc. [1]. More and more scholars adopt intelligent algorithms in path planning, such as the particle swarm optimization (PSO) [2], genetic algorithm [3; 4], ant colony algorithm [5], artificial bee colony algorithm [6; 7], and so on. These intelligent algorithms aim to overcome the limitations of traditional methods and address the core scientific challenge of enhancing trajectory precision while reducing energy consumption. [PERSON] et al. [8] use an improved B-spline interpolation method to optimize the joint trajectory of the welding robot and verify the feasibility of this method through simulation experiments. It effectively enhances the smooth continuity of the angular values and angular velocity values of each joint's trajectory, making the robot's operation smoother and more stable [9]. [PERSON] [10] and [PERSON] [11] perform kinematic analysis on the joints of the ABB IRB140 grinding robot, establish a robot model using an enhanced DH method, and deduce both forward and inverse kinematic equations through the analysis of the robot's geometric relationships and joint variables. Trajectory planning is carried out using the quintic polynomial function method, yielding improved joint trajectories and end-effector trajectory curves through simulation. In reference [12], [PERSON] et al. applied MATLAB to trajectory planning for the arc welding of a KUKA KR5 robot. The trajectory planning and simulation of the robot operation were realized utilizing the Jacobian matrix of linear paths and circular paths. The achievement of good results was tested through experimental setups. [PERSON] and others used a beetle swarm optimization algorithm for trajectory planning of robotic manipulators [3]. The beetle antennae search algorithm has distinct advantages in dealing with low-dimensional trajectory optimization problems. However, it may face efficiency issues in high-dimensional problems, such as trajectory planning for a six-axis robot, and its universality and robustness still need to be verified. [PERSON] and [PERSON] [13] propose a time-optimal trajectory planning algorithm for differential drive-wheeled mobile robots. By segmenting the trajectory and employing the bang-bang principle, it achieves rapid and safe mobility. The authors in [14; 15; 16] also propose a time-optimal trajectory planning algorithm for robot applications, achieving good results. Studies in the literature [6; 17; 18; 19; 20; 11] made corresponding trajectory planning or optimization research for different robots, which achieved certain expected results.