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A path planning algorithm for single-ended continuous planar robotic ribbon folding

Ribbon folding is a new approach to structure formation that forms higher dimensional structures using a lower dimensional primitive, namely a ribbon. In this paper, we present a novel algorithm to address path planning for ribbon folding of multi-link planar structures. We first represent the desired structure with a graph-based representation of edges and nodes. We then use graph theory to claim that for any object which is represented by a connected graph, there exists a continuous path which visits all of its edges. Finally, we develop a path planning algorithm that takes into account the physical constraints of the folding machine. The input is the desired planar structure, and the output is the optimal sequence of ribbon folds for creating that structure using the minimum number of folds. The results of this algorithm are successfully used to fold various planar structures.