Freeform Assembly Planning

3D printing enables the fabrication of complex architectures by automating long sequences of additive steps. The increasing sophistication of printers, materials, and generative design promises to make geometric complexity a non-issue 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 3D 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 sugar alcohol filaments with diameters of 100-200 microns. The assembly planner allows the freeform process to be applied to arbitrarily complex parts, 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, thus opening a variety of assembly possibilities.