Mapping Actuation Pathways in Morphing Origami Structures via Graph Analysis

Origami has emerged as a promising platform for morphing structures, programmable materials, and reconfigurable robotics. Origami structures exhibit novel multistability properties, which can be programmed to target specific stable states and actuation modes between configurations. Here we use stochastic search and gradient-based optimization to map out the stable states of the origami structure; and use minimum energy path methods to characterize the folding paths between states (i.e. actuation paths). Then using shape metrics, we identify intermediate branching points and bifurcations where folding paths intersect. The interaction and connectivity between various folding paths of the origami naturally leads to a graph theoretic representation where the vertices correspond to folded configurations of interest and the edges correspond to folding paths. The graph representation which emerges leads to insights on potential actuation cycles for locomotion, and for robotic reconfiguration strategies more broadly. We conclude by highlighting mechanisms for tuning certain structural and energetic properties of the graph which may have important implications for effectively utilizing origami principles in robotics.