A New Design Method Framework for Open Origami Design Problems

Abstract

With the development of computer science and manufacturing techniques, modern origami is no longer just used for making artistic shapes as its traditional counterpart was many centuries ago. Instead, the outstanding lightweight and high flexibility of origami structures has expanded their engineering application in aerospace, medical devices, and architecture. In order to support the automatic design of more complex modern origami structures, several computational origami design methods have been established. However these methods still focus on the problem of determining a crease pattern to fold into an exact pre-determined shape. And these methods apply deductive logic and function for only one type of topological origami structure.

In order to drop the topological constraints on the shapes, this dissertation introduces the research on the development and implementation of the abductive evolutionary design methods to open origami design problems, which is asking for their designs to achieve geometric and functional requirements instead of an exact shape. This type of open origami design problem has no formal computational solutions yet.

Since the open origami design problem requires searching for solutions among arbitrary candidates without fixing to a certain topological formation, it is NP-complete in computational complexity. Therefore, this research selects the genetic algorithm (GA) and one of its variations – the computational evolutionary embryogeny (CEE) – to solve origami problems.

The dissertation made two major contributions. One contribution is on creating the GA-based/abstract design method framework on open origami design problems. The other contribution is on the geometric representation of origami designs that directs the definition and mapping of their genetic representation and physical representation. This research introduced two novel geometric representations, which are the “ice-cracking” and the pixelated multicellular representation (PMR). The proposed design methods and the adapted evolutionary operators have been testified by two open origami design problems of making flat-foldable shapes with desired profile area and rigid-foldable 3D water containers with desired volume. The results have proved the proposed methods widely applicable and highly effective in solving the open origami design problems.