Designing Optimal Origami Structures by Computational Evolutionary Embryogeny

Abstract

As the advantages of foldable or deployable structures are being discovered, research into origami engineering has attracted more focus from both artists and engineers. With the aid of modern computer techniques, some computational origami design methods have been developed. Most of these methods focus on the problem of origami crease pattern design—the problem of determining a crease pattern to realize a specified origami final shape, but do not provide computational solutions to actually developing a shape that meets some design performance criteria. This paper presents a design method that includes the computational design of the finished shape as well as the crease pattern. The origami shape will be designed to satisfy geometric, functional, and foldability requirements. This design method is named computational evolutionary embryogeny for optimal origami design (CEEFOOD), which is an extension of the genetic algorithm (GA) and an original CEE. Unlike existing origami crease pattern design methods that adopt deductive logic, CEEFOOD implements an abductive approach to progressively evolve an optimal design. This paper presents how CEEFOOD—as a member of the GA family—determines the genetic representation (genotype) of candidate solutions, the formulation of the objective function, and the design of evolutionary operators. This paper gives an origami design problem, which has requirements on the foldedstate profile, position of center of mass, and number of creases. Several solutions derived by CEEFOOD are listed and compared to highlight the effectiveness of this abductive design method.