Particle Swarm Optimization-Based Metaheuristic Design Generation of Non-Trivial Flat-Foldable Origami Tessellations With Degree-4 Vertices

Flat-foldable origami tessellations are periodic geometric designs that can be transformed from an initial configuration into a flat-folded state. There is growing interest in such tessellations, as they have inspired many innovations in various fields of science and engineering, including deployable structures, biomedical devices, robotics, and mechanical metamaterials. Although a range of origami design methods have been developed to generate such fold patterns, some non-trivial periodic variations involve geometric design challenges, the analytical solutions to which are too difficult. To enhance the design methods of such cases, this study first adopts a geometric-graph-theoretic representation of origami tessellations, where the flat-foldability constraints for the boundary vertices are considered. Subsequently, an optimization framework is proposed for developing flat-foldable origami patterns with four-fold (i.e., degree-4) vertices, where the boundaries of the unit fragment are given in advance. A metaheuristic using particle swarm optimization (PSO) is adopted for finding optimal solutions. Several origami patterns are studied to verify the feasibility and effectiveness of the proposed design method. It will be shown that in comparison with the analytical approach and genetic algorithms (GAs), the presented method can find both trivial and non-trivial flat-foldable solutions with considerably less effort and computational cost. Non-trivial flat-foldable patterns show different and interesting folding behaviors and enrich origami design.