Clustering Path Optimisation-Based 2-Opt Rapid Wax-Drawing Trajectory Planning for Industrial 3D Wax-Drawing Robots

Abstract

The tool path trajectory serves as a cornerstone of three-dimensional (3D) printing robot technology, and path optimisation algorithms are instrumental in enabling faster, more precise and higher-quality prints. This work proposes a clustering path optimisation-based 2-opt rapid wax-drawing trajectory planning method for 3D drawing robots. Firstly, the input wax-drawing image is preprocessed to extract contour information, which is then simplified into polygons. Next, the spiral and filling trajectory algorithms are used to convert the polygons into corresponding spiral and filling paths, which are modelled as nodes in the travelling salesman problem (TSP). An improved k-means++ clustering algorithm is then designed to adaptively divide the nodes into multiple clusters. Each cluster is subsequently planned using the improved ant colony optimisation (ACO) algorithm to find the shortest path. Afterwards, the nearest-neighbour algorithm is employed to connect the shortest paths of each cluster, forming an initial tool path. Finally, the 2-opt optimisation algorithm is incorporated to optimise the preliminary path, resulting in the optimal motion trajectory for the wax-drawing tool. The verification tests show that the proposed method achieves an average reduction in path length of 30.75% compared with the parallel scanning method, traditional ant colony optimisation, Christofides with 2-opt algorithm. Meanwhile, the 3D robot wax-drawing experiments demonstrate a 17.9% reduction in drawing time, significantly improving the efficiency of large-scale production and highlighting the practical value of 3D drawing robots.