Making Shapes Foldable




Xi, Zhonghua

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Recent advances in robotics engineering and material science accelerate the development of self-folding machines, the robots that can fold themselves from flat materials to functional 3D shapes. However, designing such self-folding machines remains extremely challenging. First, finding a 2D (flat) structure that can be folded back to the original 3D shape in nontrivial especially for non-convex shapes. Furthermore, whether there exists a folding motion that continuously transforms the foldable object from one state to another without self-intersection, is one of the major concerns but rarely explored area in self-folding robots. In this dissertation, I study both unfolding and folding problems for two types of foldable objects: rigid origami and nets of Polyhedra. I make three main contributions throughout the dissertation: 1) Consider motion in foldability optimization when designing foldable objects; 2) Make both unfolding and folding easier for the machine (algorithm) and human folders via a new geometric data structure and a new foldability-aware segment strategy; 3) Propose a novel approach to compress an object with thick surface material to its most compact form via stacking. This super compressed form enables the manufacturing (such as 3D-printing) and transportation of large object in a significantly smaller space.



Computer science, Folding, Motion planning, Origami, Paper Crafting, Shape Segmentaion, Unfolding