Gradient Flow Approach for Pose Estimation of Quadratic Surface

Abstract

A key problem in robotics is the es- timation of the location and orientation of objects from surface measurement data. This is termed pose estimation. Our pose estimation problem is converted to a non-linear optimization problem that minimize an error objective function between the measured surface data and one of CAD model. The authors study gradient flows on the Lie groups to- ward 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)xR3 is de- rived and converge to an equilibrium point as usual steeplest decent methods. Discretizations of flow lead to recursive numerical methods for pose esti- mation.