Gradient flow approach for pose estimation of quadratic surface [robotics control

Abstract

A key problem in robotics is the estimation of the location and orientation of objects from surface measurement data. This is termed pose estimation. The authors' pose estimation problem is converted to a nonlinear optimization problem that minimizes an error objective function between the measured surface data and one of a CAD model. The authors study gradient flows on the Lie groups toward a solution of the pose estimation problem of quadratic surfaces. In this paper, the projected gradient flow of the objective function onto the manifold SO(3)/spl times/R/sup 3/ is derived and converge to an equilibrium point as is usual in steepest descent methods. Discretizations of flow lead to recursive numerical methods for pose estimation.