Resource-Constrained Scheduling For Multi-Robot Cooperative Three-Dimensional Printing

Cooperative three-dimensional (3D) printing (C3DP)-a representative realization of cooperative manufacturing (CM)-is a novel approach that utilizes multiple mobile 3D printing robots for additive manufacturing (AM). It makes the make-span much shorter compared with traditional 3D printing due to parallel printing. In C3DP, collision-free scheduling is critical to the realization of cooperation and parallel operation among mobile printers. In the extant literature, there is a lack of methods to schedule multi-robot C3DP with limited resources. This study addresses this gap with two methods. The first method, dynamic dependency list algorithm (DDLA), uses a constraint-satisfaction approach to eliminate solutions that could result in collisions between robots and collisions between robots with already-printed materials. The second method, modified genetic algorithm (GA), uses chromosomes to represent chunk assignments and utilizes GA operators, such as the crossover and mutation, to generate diverse print schedules while maintaining the dependencies between chunks. Three case studies, including two large rectangular bars in different scales and a foldable sport utility vehicle (SUV), are used to demonstrate the effectiveness and performance of the two methods. The results show that both methods can effectively generate valid print schedules using a specified number of robots while attempting to minimize the make-span. The results also show that both methods generate a print schedule with equal print time for the first two case studies with homogeneous chunks. In contrast, the modified GA outperforms the DDLA in the third case study, where the chunks are heterogeneous in volume and require different times to print.