Plan folding motion for rigid self-folding machine via discrete domain sampling

Self-folding robot is usually modeled as rigid origami, a class of origami whose entire surface remains rigid during folding except at crease lines. In this work, we focus on finding valid folding motion that brings the origami from the unfolded state continuously to the folded state. Although recent computational methods allow rapid simulation of folding process of certain rigid origami, these methods can fail even when the input crease pattern is extremely simple but requires implicit folding orders. Moreover, due to the rigidity requirement, the probability of generating a valid configuration via uniform sampling is zero, which greatly hinders the applicability of traditional sampling-based motion planners. We propose a novel sampling strategy that samples in the discrete domain. Our experimental results show that the proposed method could efficiently generate valid configurations. Using those configurations, the planner successfully folds several types of rigid origami that the existing methods fail to fold and could discover multiple folding paths in different homotopies.