Continuous unfolding of polyhedra - a motion planning approach

Cut along the surface of a polyhedron and unfold it to a planar structure without overlapping is known as Unfolding Polyhedra problem which has been extensively studied in the mathematics literature for centuries. However, whether there exists a continuous unfolding motion such that the polyhedron can be continuously transformed to its unfolding has not been well studied. Recently, researchers started to recognize continuous unfolding as a key step in designing and implementation of self-folding robots. In this paper, we model the unfolding of a polyhedron as multi-link tree-structure articulated robot, and address this problem using motion planning techniques. Instead of sampling in continuous domain which traditional motion planners do, we propose to sample only in the discrete domain. Our experimental results show that sampling in discrete domain is efficient and effective for finding feasible unfolding paths.