Homography estimation is an important task in robotics applications, such as landing on moving platforms, docking and refueling, building inspection, and so on. Nonlinear observers depend on an estimate of the group algebra velocity as a feed-forward 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 article proposes a solution for the case where the motion is periodic, or approximately periodic, with a 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 this article lies in formalizing the internal model for observer design to the noncompact Lie group SL(3) and providing a demonstration of the effectiveness of the approach with real-world examples.

中文翻译：

---

基于直接点对应的移动平面场景的单应估计

在机器人应用程序中，例如在移动平台上着陆，对接和加油，建筑物检查等方面，单应性估计是一项重要任务。非线性观测器依赖于组代数速度的估计作为前馈项，以最大程度地减少滤波器响应中的滞后。当摄像机和场景都在移动时，并且对于透视图像构造（如单应性），通常不可能直接测量所需的组速度。本文为运动是周期性的或近似周期性的已知周期的情况提出了一种解决方案。该方法基于内部模型原理，其中内部模型可以扩展为包括所需周期的足够谐波，以便对复杂的周期性运动进行建模。