  There is increasing demand for automated systems that can fabricate 3D
structures. Robotic spatial extrusion has become an attractive alternative to
traditional layer-based 3D printing due to a manipulator's flexibility to print
large, directionally-dependent structures. However, existing extrusion planning
algorithms require a substantial amount of human input, do not scale to large
instances, and lack theoretical guarantees. In this work, we present a rigorous
formalization of robotic spatial extrusion planning and provide several
efficient and probabilistically complete planning algorithms. The key planning
challenge is, throughout the printing process, satisfying both stiffness
constraints that limit the deformation of the structure and geometric
constraints that ensure the robot does not collide with the structure. We show
that, although these constraints often conflict with each other, a greedy
backward state-space search guided by a stiffness-aware heuristic is able to
successfully balance both constraints. We empirically compare our methods on a
benchmark of over 40 simulated extrusion problems. Finally, we apply our
approach to 3 real-world extrusion problems.
