An End-to-End Approach to Self-Folding Origami Structures

This paper presents an end-to-end approach to automate the design and fabrication process for self-folding origami structures. Self-folding origami structures are robotic sheets composed of rigid tiles and joint actuators. When they are exposed to heat, each joint folds into a preprogrammed angle. Those folding motions transform themselves into a structure, which can be used as body of 3-D origami robots, including walkers, analog circuits, rotational actuators, and microcell grippers. Given a 3-D model, the design algorithm automatically generates a layout printing design of the sheet form of the structure. The geometric information, such as the fold angles and the folding sequences, is embedded in the sheet design. When the sheet is printed and baked in an oven, the sheet self-folds into the given 3-D model. We discuss, first, the design algorithm generating multiple-step self-folding sheet designs, second, verification of the algorithm running in <inline-formula><tex-math notation="LaTeX">$O(n^2)$</tex-math> </inline-formula> time, where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of the vertices, third, implementation of the algorithm, and finally, experimental results, several self-folded 3-D structures with up to 55 faces and two sequential folding steps.