Plan Folding Motion for Rigid Origami via Discrete Domain Sampling

Zhonghua Xi and Jyh-Ming Lien


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 a valid folding motion that brings the origami from the unfolded state continuously to the folded state. Although recent computational methods allow rapid simulation of the folding process of certain rigid origamis, these methods can fail even when the input crease pattern is extremely simple but with implicit folding orders. Moreover, due to the rigidity requirement, the probability of generating a valid configuration via uniform sampling is zero, which greatly hinders that 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 planners successfully fold several types of rigid origamis that the existing methods fail to fold and could discover multiple folding paths for Multi-DOF origamis.


We show valid configurations of many origami usually form a manifold in lower dimensional space as in the figure below, thus instead of sampling in the continuous domain with zero probability to generate a valid configuration, we sample in the discrete domain which allows us to generate valid and important intermediate configurations.

image image image
Valid configuration space (shown in blue) of a single vertex multi-DOF Waterbomb crease pattern under various deformation upper bound.




Folding process of a Sailboat crease pattern found the proposed method.



Top: folding path found by FROG. Bottom: alternative folding path found by the proposed method.


Plan Folding Motion for Rigid Origami via Discrete Domain Sampling, Zhonghua Xi and Jyh-Ming Lien, 2015 IEEE International Conference on Robotics and Automation (ICRA), May. 2015
Web Site / Paper (pdf) / BibTeX

Plan Folding Motion for Rigid Origami via Discrete Domain Sampling, Zhonghua Xi and Jyh-Ming Lien, Department of Computer Science, George Mason University, (Technical Report), 2015
Web Site / Paper (pdf) / BibTeX

Related Works

List of MASC Research Pages / List of MASC Origami Pages
Computer Science @ George Mason University