Motion planning and control of a planar polygonal linkage

For a polygonal linkage, we produce a fast navigation algorithm on its configuration space. The basic idea is to approximate $M(L)$ by the vertex-edge graph of the cell decomposition of the configuration space discovered by the first author. The algorithm has three aspects: (1) the number of navigation steps does not exceed 14 (independent on the number of edges), (2) each step is a disguised flex of a quadrilateral from one triangular configuration to another, which can be ranged as well understood type of flexes, and (3) each step can be performed in a mechanical way.