Propagation of Orientation Uncertainty of 3D Rigid Object to Its Points

If a CAD model of a rigid object is available, the location of any point on an object can be derived from the measured 6DOF pose of the object. However, the uncertainty of the measured pose propagates to the uncertainty of the point in an anisotropic way. We investigate this propagation for a class of systems that determine an object pose by using point-based rigid body registration. For such systems, the uncertainty in the location of the points used for registration propagates to the pose uncertainty. We find that for different poses of the object, the direction corresponding to the smallest propagated uncertainty remains relatively unchanged in the object's local frame, regardless of object pose. We show that this direction may be closely approximated by the moment of inertia axis which is based on the configuration of the fiducials. We use existing theory of rigid-body registration to explain the experimental results, discuss the limitations of the theory and practical implications of our findings.