Abstract
A key problem in robotics is the estimation of the location and orientation of 3-D curved objects from surface measurement data. This is termed pose estimation. We assume that parts of 3-D curved objects are approximated to quadratic surfaces. Fundamental task is to estimate the pose of quadratic surface from measured data. A solutions for this task facilitates pose estimation for more complex object. Our pose estimation problem is converted to a non-linear optimization problem that minimize an error objective function between the measured surface data and the one of CAD model. The authors study gradient flows on the Lie groups towards 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 converses to an equilibrium point as usual steepest decent methods. Discretizations of the flow leads to recursive numerical methods for pose estimation. The proposed algorithm has been tested to show its validity using synthetic and real data.
