Algorithms for solving reachability problems in 2-link planar arms using Grobner bases

It is a crucial problem to study the reachability of planar arms inside convex obtuse polygons. In this paper, we studied the reachability problem for 2-link planar arms inside a circle, a general polygon with (without) some holes in it and presented several algorithms for them. Furthermore, we proposed some algorithms for a special case where the shoulder of an arm moves along a given segment or passes through a certain path. It is essential to mention that our approach is based on the Gro¨bner bases technique.