Locating Polyhedral Objects from Edge Point Data

Abstract

A method is presented to locate a general polyhedron in space with six degrees of freedom. A light stripe sensor is assumed to be capable of providing three-dimensional data points on known edges of the polyhedron to within a known accuracy. A representation is found for all the ways three line segments of fixed length can fall between the edges of a polyhedron. This representation, called an edge interval, is used in a tree search to find the location of each data point to within an interval on the edge. The final location of the object is determined by a one-dimensional line search. The method is illustrated with simulated data from a unit tetrahedron and results from a computer implementation are presented. The tree search takes a negligible amount of time and the one-dimensional line search takes a small additional increment.