Motion planning and control of a planar polygonal linkage
This work addresses motion planning for polygonal linkages, which is a domain-specific problem in robotics and computational geometry, and appears incremental as it builds on prior cell decomposition methods.
The paper tackles the problem of navigating the configuration space of a planar polygonal linkage by developing a fast algorithm that approximates this space using a vertex-edge graph from a cell decomposition. The result is an algorithm with at most 15 navigation steps, each involving a well-understood quadrilateral flex, and it can be performed explicitly by adding extra bars to create a one-degree-of-freedom mechanism.
For a polygonal linkage, we produce a fast navigation algorithm on its configuration space. The basic idea is to approximate the configuration space by the vertex-edge graph of its cell decomposition discovered by the first author. The algorithm has three aspects: (1) the number of navigation steps does not exceed 15 (independent of the linkage), (2) each step is a disguised flex of a quadrilateral from one triangular configuration to another, which is a well understood type of flex, and (3) each step can be performed explicitly by adding some extra bars and obtaining a mechanism with one degree of freedom.