Study on Trajectory Planning for Polishing Free-Form Surfaces of XY-3-RPS Hybrid Robot

Free-form surface polishing is a key process in precision machining within high-end manufacturing, where optimizing the polishing trajectory directly influences both processing quality and efficiency. Traditional trajectory planning methods for free-form surface polishing in high-curvature regions suffer from issues such as a lack of precision, low trajectory continuity, and inefficiency. This paper proposes an improved trajectory planning method based on curvature characteristics, incorporating dynamic partitioning and boundary smoothing algorithms. These methods dynamically adjust according to surface curvature, enhancing processing efficiency and surface quality. Additionally, a hybrid optimization framework combining a genetic algorithm (GA) and local search (LS) is proposed to address the challenges of balancing global optimization with local fine-tuning in traditional trajectory planning methods. These challenges often result in large errors, low machining efficiency, and unstable surface quality. The method optimizes the overall trajectory distribution through a global search using GA while locally refining the high-curvature regions with LS. This combination improves trajectory uniformity and smoothness, and the results demonstrate significant increases in machining efficiency and accuracy. Finally, the feasibility of the trajectory planning method was verified through motion simulation. This paper also provides a detailed description of the mathematical modeling, algorithm implementation, and simulation analysis of the XY-3-RPS hybrid robot for trajectory optimization, offering both a theoretical foundation and engineering support for its application in free-form surface polishing.