A multi-functional fiber positioning system for extremely large telescopes

We present a conceptual design for a fiber positioning system for multi-object high-resolution spectroscopy, designed to be compatible with the upcoming large telescopes with a wide field of view. The design incorporates multiple Atmospheric Dispersion Correctors (ADCs) and tip-tilt mirrors that receive non-telecentric input from individual targets and direct it to the ADCs. Here, we introduce a mechanical design for the fiber positioner that accommodates the optics and operates in a curved focal plane with a Radius of Curvature (R) of 3m. This mechanical design provides four degrees of freedom to access the focal volume, enhancing targeting efficiency. The proposed design and an efficient target allocation algorithm ensure a targeting efficiency of approximately 80-100% for a primary observation session. We also present a methodology for target assignment, positioning, and quantification based on sequential and Monte Carlo (MC) algorithms. This method has been tested on realistic fields with varying target densities to validate its performance.