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Abstract We present NoodlePrint, a generalized computational framework for maximally concurrent layer-wise cooperative 3D printing (C3DP) of arbitrary part geometries with multiple robots. NoodlePrint is inspired by a recently discovered set of helically interlocked space-filling shapes called VoroNoodles. Leveraging this unique geometric relationship, we introduce an algorithmic pipeline for generating helically interlocked cellular segmentation of arbitrary parts followed by layer-wise cell sequencing and path planning for cooperative 3D printing. Furthermore, we introduce a novel concurrence measure that quantifies the amount of printing parallelization across multiple robots. Consequently, we integrate this measure to optimize the location and orientation of a part for maximally parallel printing. We systematically study the relationship between the helix parameters (i.e., cellular interlocking), the cell size, the amount of concurrent printing, and the total printing time. Our study revealed that both concurrence and time to print primarily depend on the cell size, thereby allowing the determination of interlocking independent of time to print. To demonstrate the generality of our approach with respect to part geometry and the number of robots, we implemented two cooperative 3D printing systems with two and three printing robots and printed a variety of part geometries. Through comparative bending and tensile tests, we show that helically interlocked part segmentation is robust to gaps between segments. 

Abstract One of the major challenges in 3D printing is its lack of scalability both in size and speed, which directly impacts its economic feasibility for large-scale industrial applications. Cooperative 3D printing (C3DP) is an emerging paradigm that aims to address these issues by employing multiple mobile printers that work in parallel. However, a crucial step in enabling C3DP is the development of a collision-free communication framework between the printers during the manufacturing process. Many C3DP systems found in the literature develop solutions for collision-free printing that are specific to the setup being used, thus not allowing the solution to be transferred to other similar systems. In this paper, we formulate a general framework that generates four distinct collision-free communication strategies to enable arm-arm coordination for C3DP using robotic manipulators. We considered collisions both between the arms with themselves and between the arms and the part being printed. The strategies are general in that they are agnostic to the number of printers, their kinematics, and their spatial configurations in the manufacturing environment. We conducted a study of the four strategies using a two-printer scenario and then physically validated them with four test cases of varying geometries. The results show that the strategies successfully produce printed parts while being collision-free. The makespan reduction using our strategies when compared to a single printer varied from 20% to 42% depending on the strategy used. Finally, we discuss the limitations of the framework, as well as future research directions. 

Cooperative 3D Printing (C3DP), an additive manufacturing platform consisting of a swarm of mobile printing robots, is an emerging technology designed to address the size and printing speed limitations of conventional, gantry-based 3D printers. A typical C3DP process often involves several interconnected stages, including project/job partitioning, job placement on the floor, task scheduling, path planning, and motion planning. In our previous work on project partitioning, we presented a Z-Chunker, which vertically divides a tall print project into multiple jobs to overcome the physical constraints of printers in the Z direction, and an XY Chunker, to partition jobs into discrete chunks, which are allocated to individual printing robots for parallel printing. These geometry partitioning algorithms determine what is to be printed, but other information, such as when, where, and in what order chunks should be printed, is required to carry out the print physically. This paper introduces the first Job Placement Optimizer for C3DP based on Dynamic Dependency List schedule assignment and Conflict-Based Search path planning. Our algorithm determines the optimal locations for all jobs and chunks (i.e., subtasks of a job) on the factory floor to minimize the makespan for C3DP. To validate the proposed approach, we conduct three case studies: a simple geometry with homogeneous jobs in the Z direction and two complex geometries (one with moderate complexity and one relatively more complex) with non-homogeneous jobs in the Z direction. We also performed simulations to understand the impact of other factors, such as the number of robots, the number of jobs, chunking orientation, and the heterogeneity of prints (e.g., when chunks are different in size and materials), on the effectiveness of this placement optimizer. 

Abstract In this paper, we present a decentralized approach based on a simple set of rules to schedule multi-robot cooperative additive manufacturing (AM). The results obtained using the decentralized approach are compared with those obtained from an optimization-based method, representing the class of centralized approaches for manufacturing scheduling. Two simulated case studies are conducted to evaluate the performance of both approaches in total makespan. In the first case, four rectangular bars of different dimensions from small to large are printed. Each bar is first divided into small subtasks (called chunks), and four robots are then assigned to cooperatively print the resulting chunks. The second case study focuses on testing geometric complexity, where four robots are used to print a mask stencil (an inverse stencil, not face covering). The result shows that the centralized approach provides a better solution (shorter makespan) compared to the decentralized approach for small-scale problems (i.e., a few robots and chunks). However, the gap between the solutions shrinks while the scale increases, and the decentralized approach outperforms the centralized approach for large-scale problems. Additionally, the runtime for the centralized approach increased by 39-fold for the extra-large problem (600 chunks and four robots) compared to the small-scale problem (20 chunks and four robots). In contrast, the runtime for the decentralized approach was not affected by the scale of the problem. Finally, a Monte-Carlo analysis was performed to evaluate the robustness of the centralized approach against uncertainties in AM. The result shows that the variations in the printing time of different robots can lead to a significant discrepancy between the generated plan and the actual implementation, thereby causing collisions between robots that should have not happened if there were no uncertainties. On the other hand, the decentralized approach is more robust because a collision-free schedule is generated in real-time.