3D Shape Reconstruction of Small Bodies From Sparse Features

Abstract

The autonomous approach of spacecraft to a small body (comet or asteroid) relies on using all available information at each phase of the approach. This letter presents new algorithms for global shape reconstructions from sparse tracked surface points. These methods leverage estimates from earlier phases, such as rotation pole, as well as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge, such as a genus-0 body (i.e. without boundaries or topological holes). A mapping algorithm is proposed, which performs faithful reconstructions while enforcing genus-0 output through spherical parameterization. To estimate the shape of permanently shadowed regions of the body, a symmetry reconstruction method is added to the reconstruction algorithms. This method is shown to substantially increase the reconstruction accuracy but is subject to the symmetry of the body perpendicular to the rotation pole. The proposed mapping algorithm is compared to state-of-the-practice surface reconstruction algorithms, assessing their accuracy and ability to correctly generate genus-0 shape models for 2400 datasets and three small bodies. The proposed spherical parameterization algorithm performed consistently with the state-of-the-practice while being the only algorithm to always produce genus-0 shape models.