A New Collision Avoidance Fiber Assignment Algorithm for Robotic Fiber Positioners in Multi-Object Spectroscopy

We present a new fiber assignment algorithm for a robotic fiber positioner system in multi-object spectroscopy. Modern fiber positioner systems typically have overlapping patrol regions, resulting in the number of observable targets being highly dependent on the fiber assignment scheme. To maximize observable targets without fiber collisions, the algorithm proceeds in three steps. First, it assigns the maximum number of targets for a given field of view without considering any collisions between fiber positioners. Then, the fibers in collision are grouped, and the algorithm finds the optimal solution resolving the collision problem within each group. We compare the results from this new algorithm with those from a simple algorithm that assigns targets in descending order of their rank by considering collisions. As a result, we could increase the overall completeness of target assignments by 10% with this new algorithm in comparison with the case using the simple algorithm in a field with 150 fibers. Our new algorithm is designed for the All-sky SPECtroscopic survey of nearby galaxies (A-SPEC) based on the K-SPEC spectrograph system, but can also be applied to similar fiber-based systems with heavily overlapping fiber positioners.