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

TL;DR

This paper tackles maximizing target completeness in fiber-fed multi-object spectrographs with heavily overlapping patrol regions while avoiding fiber collisions. It introduces a three-step approach: first assign as many targets as possible ignoring collisions, then group colliding fibers and optimize within each group using parallel processing and boundary-splitting via K-means. The method yields about a 10% gain in completeness over a simple collision-aware algorithm in a 150-fiber field and yields overall completeness around 80%, potentially reaching ~90% when existing redshifts are used, making it practical for large all-sky surveys like A-SPEC. While tailored to K-SPEC, the algorithm is generalizable to other MOS systems with overlapping two-armed positioners and supports integration with trajectory planning and metrology for deployment in the 2026 commissioning.

Abstract

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.

Figures (8)

• Figure 1: A schematic view of K-SPEC system
• Figure 2: K-SPEC robotic fiber positioners. $\it left$: Side view of a single-unit fiber positioner, which comprises a beta (upper) arm and an alpha (lower) arm that rotate independently. $\it right$: Top view of a collection of seven fibers arranged in a hexagonal array.
• Figure 3: Configuration of K-SPEC fiber positioners. The black dots represent base positions of the robotic fiber positioners. The gray-shaded regions denote the patrol areas of fiber positioners, with varying opacities indicating different levels of overlap. The blue triangles and the red circle represent the fiducials and guide camera, respectively.
• Figure 4: A schematic diagram that illustrates the fiber collision. The dashed and solid lines represent the alpha and beta arms, respectively. The blue shades describe the width of beta arms. The red dot-dashed line indicates the collision buffer $\left(\sigma_{cb}\right)$ of a single fiber positioner, which collides with another fiber positioner.
• Figure 5: A flowchart of the algorithm.