Signed distance field-based collision-free trajectory planning for on-machine measurement of conical covers

Abstract

To address the inefficiency in collision detection and computational challenges in interference quantification during on-machine measurement of conical covers, this paper proposes a signed distance field-based trajectory planning methodology. A hierarchical detection framework is developed through: 1) A coarse detection phase combining oriented bounding boxes with octree spatial indexing and the separating axis theorem for rapid collision zone localization; 2) A refined detection stage utilizing normal vector-corrected signed distance field integrated with k-d tree acceleration for precise interference computation, coupled with an interference-pose mapping model to optimize probe orientation. Experimental results demonstrate that the proposed normal vector-corrected signed distance field preserves signed distance continuity in high-curvature regions of freeform surfaces, enabling high-precision identification of collision states. Validation against VERICUT simulations demonstrates 100 % detection accuracy in collision zones and 97.3 % accuracy in safety threshold intervals. The proposed method achieves 27 % and 47 % detection speed improvements over the k-d tree-accelerated Euclidean distance algorithm and the k-d tree-accelerated signed distance field method, respectively. Practical on-machine trials confirm collision-free measurement in areas of high collision risk. This work provides a novel method for ensuring detection accuracy and detection speed in complex geometry inspection.