## Geometric sensing of known planar shapes (1996)

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Venue: | In Proceedings of the 1996 IEEE International Conference on Robotics and Automation |

Citations: | 19 - 10 self |

### BibTeX

@INPROCEEDINGS{Jia96geometricsensing,

author = {Yan-bin Jia and Michael Erdmann},

title = {Geometric sensing of known planar shapes},

booktitle = {In Proceedings of the 1996 IEEE International Conference on Robotics and Automation},

year = {1996},

pages = {165--171}

}

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### 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 article we investigate two problems of determining the pose of a polygonal part of known shape for the cases of a continuum and a finite number of possible poses respectively. The first problem, named sensing by inscription, involves determining the pose of a convex n-gon from a set of m supporting cones. An algorithm with running time O(nm) that almost always reduces to O(n+m log n) is presented to solve for all possible poses of the polygon. We prove that the number of possible poses cannot exceed 6n, given m ≥ 2 supporting cones with distinct vertices. Simulation 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. On many occasions a parts feeder will have reduced the number of possible poses of a part to a small finite set. Our second problem, named sensing by point sampling,