Estimate pose deviation of on-orbit deployable mechanisms based on cross-ratio invariability

With the rapid development of space science projects, large deployable mechanisms have been widely used. However, due to the effects of mechanical friction and gravitational acceleration, on-orbit mechanisms cannot be always deployed to the expected pose. For some precision optical mechanisms, even a minor deviation can result in significant error, so it needs to be measured and corrected. In this paper, the deployment process was modeled and simplified as rotation under single-rotation-axis constraint and translation under single-direction constraint. To solve the problem, a method based on cross-ratio invariability was proposed. The proposed method does not rely on camera calibration techniques, as well as artificial marking points, both of which are necessary in PnP. Instead, only three calibration images before launch and a measurement image on orbit were required. Simulations and experiments demonstrated that the proposed method is more accurate than PnP. In addition, experiments also proved that the feasibility of the proposed method under dark conditions with the aid of a light source and some reflective marking points.