Folding and unfolding origami tessellation by reusing folding path

Recent advances in robotics engineering have enabled the realization of self-folding machines. Rigid origami is usually used as the underlying model for the self-folding machines whose surface remains rigid during folding except at joints. A key issue in designing rigid origami is foldability that concerns about finding folding steps from a flat sheet of crease pattern to a desired folded state. Although recent computational methods allow rapid simulation of folding process of certain rigid origamis, these methods can fail even when the input crease pattern is extremely simple. In this paper, we take on the challenge of planning folding and unfolding motion of origami tessellations, which are composed of repetitive crease patterns. The number of crease lines of a tessellation is usually large, thus searching in such a high dimensional configuration space with the requirement of maintaining rigidity is nontrivial. We propose a motion planner that takes symmetry into consideration and reuses folding path found on the essential crease pattern. Both of these strategies enable us to fold large origami tessellation much more efficiently than existing methods. Our experimental results show that the proposed method successfully folds several types of rigid origami tessellations that existing methods fail to fold.