LAUSR

3-D printing enables the fabrication of complex architectures at multiple length scales by automating large sequences of additive steps. The increasing sophistication of printers, materials, and generative design promise to make geometric complexity a nonissue in manufacturing; however, this complexity can only be realized if a design can be translated into a physically executable sequence of printing operations. We investigate this planning problem for freeform direct-write assembly, in which filaments of material are deposited through a nozzle translating along a 3-D path to create sparse, frame-like structures. We enumerate the process constraints for different variants of the freeform assembly process and show that, in the case where material stiffens via a glass transition, determining whether a feasible sequence exists is NP-complete. Nonetheless, for topologies typically encountered in real-world applications, finding a feasible or even optimal sequence is a tractable problem. We develop a sequencing algorithm that maximizes the fidelity of the printed part and minimizes the probability of print failure by modeling the assembly as a linear, elastic frame. We implement the algorithm and validate our approach experimentally, printing objects composed of thousands of large-aspect-ratio sugar alcohol filaments with diameters of 100– $200~\mu \text{m}$ . Note to Practitioners—Extrusion-style 3-D printers typically pattern material in a series of 2-D layers, but they can be also be programmed to deposit material along 3-D paths in a “freeform” fashion. However, programming a printer to operate in this way requires consideration of constraints related to collision and stability. For large designs, finding an optimal or even feasible plan with respect to these constraints requires automated planning. We address a hard version of this problem in which any joint in the frame can only support one cantilever at a time. We develop an exact algorithm that maximizes the robustness of the printing plan and validate it by printing complex freeform designs. The assembly planner allows the freeform process to be applied to arbitrarily complex parts, with applications ranging from tissue engineering and microfluidics at the micrometer scale, to vascularized functional materials and soft robots at the millimeter scale, to structural components at the meter scale. This approach removes a major bottleneck in the workflow for freeform assembly, allowing scientists and engineers to automatically translate complex freeform designs into optimal printing plans.