A Heuristic Sequencing Method for Time Optimal Tracking of Open and Closed Paths

Tracking sequences of predefined open and closed paths is of crucial interest for applications like laser cutting and similar production processes. The disconnected paths are connected by non-productive, four times continuously differentiable trajectories, which also account for the overall process time. Heuristic methods are applied in order to find a proper sequencing of the open and closed path and thereby minimize the overall process time while respecting constraints given by the system limits. To this end, the exact traversing times of the non-productive linking trajectories are computed, which also have to be time optimal subject to the system limits. Finally, two heuristic algorithms are presented and compared with respect to solution quality and calculation time using randomly generated problems.