### Sensing Polygon Poses by Inscription

**Yan-Bin Jia** and **Michael Erdmann**

*1994 IEEE International Conference on Robotics and Automation*

* Abstract *

Industrial assembly involves sensing the pose (orientation and
position) of a part. Efficient and reliable sensing strategies can be
developed for an assembly task if the shape of the part is known in
advance. In this paper we investigate the problem of determining the
pose of a convex *n*-gon from a set of *m* supporting cones, i.e.,
cones with both sides supporting the polygon. An algorithm with
running time *O*(*nm*) which almost always reduces to
*O*(*n* + *m* log *n*) is
presented to solve for all possible poses of the polygon. As a
consequence, the *polygon inscription* problem of finding all
possible poses for a convex *n*-gon inscribed in another convex
*m*-gon, can be solved within the same asymptotic time bound. We prove
that the number of possible poses cannot exceed 6*n*, given
*m* >= 2 supporting cones with distinct vertices. Experiments demonstrate
that two supporting cones are sufficient to determine the real pose of the
*n*-gon in most cases.
Our results imply that sensing in practice can be carried out by
obtaining viewing angles of a planar part at multiple exterior sites
in the plane. As a conclusion, we generalize this and other sensing
methods into a scheme named *sensing by inscription*.