Synthesis of Fast and Collision-free Folding of Polyhedral Nets

A predominant issue in the design and fabrication of highly non-convex polyhedral structures through self-folding, has been the collision of surfaces due to inadequate controls and the computational complexity of folding-path planning. We propose a method that creates linearly foldable polyhedral nets, a kind of unfoldings with linear collision-free folding paths. We combine the topological and geometric features of polyhedral nets into a hypothesis fitness function for a genetic-based unfolder and use it to map the polyhedral nets into a low dimensional space. An efficient learning strategy is used to optimize the fitness function to produce the optimal nets. We experimentally demonstrate that the proposed method can find linearly foldable nets for highly non-convex polyhedra with substantial complexity. The technique presented in the paper will provide a powerful tool to enable designers, materials engineers, roboticists, to name just a few, to make physically conceivable structures through self-assembly by eliminating the common self-collision issue. It also simplifies the design of the control mechanisms when making deployable shape morphing devices. Additionally, our approach makes foldable papercraft more accessible to younger children and provides chances to enrich their education experiences.