Homography Estimation of a Moving Planar Scene from Direct Point Correspondence

Homography estimation is an important task in robotics applications such as landing on moving platforms, docking and refueling, building inspection, etc. Non-linear observers depend on an estimate of the group algebra velocity as a feedforward term to minimize lag in the filter response. When both the camera and the scene are moving, and for perspective image constructs such as the homography, it is often impossible to directly measure the required group velocity. This paper proposes a solution for the case where the motion is periodic, or approximately periodic, with known period. The approach is based on the internal model principle, where the internal model can be expanded to include a sufficient harmonics of the desired period in order to model complex periodic motions. The novelty of the work lies in formalizing the internal model for observer design to the non-compact Lie group SL(3) and providing a demonstration of the effectiveness of the approach with real world examples.