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

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)×R³ 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