Robotics have recently contributed to cosmological spectroscopy to automatically obtain the map of the observable universe using robotic fiber positioners. For this purpose, an assignment algorithm is required to assign each robotic fiber positioner to a target associated with a particular observation. The assignment process directly impacts on the coordination of robotic fiber positioners to reach their assigned targets. In this paper, we establish an optimal target assignment scheme which simultaneously provides the fastest coordination accompanied with the minimum of colliding scenarios between robotic fiber positioners. In particular, we propose a cost function by whose minimization both of the cited requirements are taken into account in the course of a target assignment process. The applied simulations manifest the improvement of convergence rates using our optimal approach. We show that our algorithm scales the solution in quadratic time in the case of full observations. Additionally, the convergence time and the percentage of the colliding scenarios are also decreased in both supervisory and hybrid coordination strategies.

中文翻译：

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大规模光谱调查的最佳目标分配

机器人技术最近为宇宙光谱学做出了贡献，以使用机器人光纤定位器自动获取可观测宇宙的地图。为此，需要分配算法将每个机器人光纤定位器分配给与特定观察相关的目标。分配过程直接影响机器人光纤定位器的协调以达到其分配的目标。在本文中，我们建立了一个最佳目标分配方案，该方案同时提供了最快的协调，同时将机器人光纤定位器之间的碰撞场景降至最低。特别是，我们提出了一个成本函数，通过它在目标分配过程中最小化所引用的两个要求。应用的模拟表明使用我们的最佳方法提高了收敛速度。我们展示了我们的算法在完整观测的情况下以二次时间缩放解。此外，在监督和混合协调策略中，收敛时间和碰撞场景的百分比也降低了。