Cooperative 3D printing (C3DP) with multiple robotic manipulators can reduce build time through parallel deposition, but it requires layer partitioning that accounts for collision clearance, workload balance, G-code toolpath compatibility, and interlayer boundary alignment. This study presents a Voronoi- and graph-based layer partitioning framework for C3DP. STL geometry and G-code were integrated into layer-aligned data, and a 65 mm collision clearance was defined from the measured end-effector collision radius as the minimum separation preventing collisions between robots approaching nonadjacent Voronoi cells. Each layer was divided into Voronoi cells so that non-adjacent cells could be treated as collision-free regions. Cell adjacency and toolpath-based processing time were modeled as a weighted graph, and adjacent cells were clustered into workload-balanced task regions. Interlayer seed offsets staggered the partition boundaries, and graph coloring identified regions that could be printed simultaneously.The framework was evaluated by workload-balance simulations and printing experiments. Balance deteriorated when clusters were excessive relative to graph nodes. In experiments, the end-effector separation always exceeded the 65 mm clearance. Partitioned printing reduced the layer printing time from 70.063 to 63.57 min, a 9.3% reduction, and the second layer covered the preceding partition boundary, confirming the staggered-boundary implementation.

Predicting the response of a system, even several steps ahead, offers tremendous advantage to improve the system performance, to acquire an ideal model of a system and disturbances. The best way of predicting a response signal from a system is to use the sinusoidal extrapolation based on its frequency characteristics. Sinusoidal extrapolation is a statistical method for predicting future data through frequency analysis of past data. Practically speaking, the prediction from a frequency analysis in a control system is appropriate, because the output of a system can be modeled by several dominant frequencies from input and system models. In this study, we developed a novel and reliable prediction filter, using multi frequency sinusoidal extrapolation and a prediction error compensation algorithm. In this paper, we also suggest the design guidelines, regularity, and overall process of obtaining optimal predictions from an efficient and practical view, for the widely used industrial equipment. Results show that the performance of the proposed prediction filter is considered reliable and effective for improving the performance of a system, such as a motion controller.