Trajectory planning for 3D printing: A revisit to traveling salesman problem

Abstract

Abstract-Three dimensional (3D) printing can be used to manufacture many different objects range from toys to hitech robot parts. This paper investigates 3D printer trajectory planning to improve the speed of the printing process. The printing speed mainly depends on the motion speed and path of the printing nozzle. We use triangular and trapezoidal velocity profiles to minimize the transition time between print segments. In this work, several algorithms that were originally proposed as solutions for conventional traveling salesman problem are modified to adapt to the new problem. The proposed modifications are designed to obtain time-efficient trajectories for the printing nozzle.

A Relaxation Scheme for TSP-Based 3D Printing Path Optimizer

“…The objective function is replaced by the time-based objective function described in Section II-C. Solutions obtained from the optimizer will undergo a refinement process using the 2-opt algorithm [11] which showed to be highly effective in [5].…”

“…A TSP-optimization will be performed to find a fast tour to visit all the centers points of the identified partitions, which also determines their order of visit. Inside each partition, the Christofides-based TSP solver with 2-opt in [5] will be used to find a fast tour. To shorten the transition segments among partitions, the virtual segment required by the method in [5] will be placed between two end points that are nearest to the centers of the adjacent partitions.…”

“…Inside each partition, the Christofides-based TSP solver with 2-opt in [5] will be used to find a fast tour. To shorten the transition segments among partitions, the virtual segment required by the method in [5] will be placed between two end points that are nearest to the centers of the adjacent partitions. This will ensure the tour will always start and end at these two selected points.…”

“…By predicting velocity errors, fluctuations in speed can be greatly reduced. In [5], Ganganath et al formulated the printing nozzle optimization problem as a traveling salesman problem (TSP). Based on their formulation, several modified TSP solving algorithms were proposed and evaluated using computer simulations.…”

“…A significant improvement is observed when comparing their proposed methods with greedy-based solvers. Fok et al in [6] further fine-tuned a Christofides-based solver in [5] and applied it to real-life 3D models. Simulation results show that their proposed algorithm can outperform Cura [7], a common open-source model slicer for 3D printers.…”