Inverse design of flat-foldable volumetric origami with smooth curved profile

Through flat-folding, origami provides an extremely compact packaging strategy for deployable structures in aerospace, architecture, and robotics. However, origami's flat, volumeless facets limit the formation of smooth curvature, restricting its applicability in systems where smooth curved geometries are essential for performance, such as aerospace and electromagnetic communication systems. Here, we propose volumetric origami that preserves smooth curvature and an inverse design method that generates flat-foldable volumetric origami for given target curved surfaces. The flat-foldability enables arbitrarily prescribed compactness in volumetric origami folding, with its stowage efficiency governed by the number of cells and the target profile. The structural integrity and engineering feasibility of volumetric origami are validated through successful flight testing of a UAV equipped with flat-foldable volumetric origami wings replicating a target airfoil. Our approach bridges the gap between planar origami and the curvature requirements of engineering systems, expanding design freedom for curved structures under stringent spatial constraints.