SDSS-V robotic focal plane system: overview of coordinate systems and transforms

The Sloan Digital Sky Survey V (SDSS-V) is an all-sky spectroscopic survey of >6 million objects, designed to decode the history of the Milky Way, reveal the inner working of the stars, investigate the origin of solar systems, and track the growth of supermassive black holes across the Universe. Here we describe the mathematical framework behind the SDSS-V robotic Focal Plane System (FPS), specifically the coordinate systems and transforms used to propagate locations of targets from astronomical catalogs to coordinates on a robotically positioned fiber or guide camera. This framework provides the backbone for the design and operations of SDSS-V's MOS surveys. All coordinate systems and transformations between them are provided in SDSS-V's coordio software package.