Collision Probability Evaluation of LAMOST Robotic Fiber Positioners in the Design Phase

Abstract Multiobject spectroscopic telescopes are crucial for modern astronomy. Among them, the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST), with thousands of robotic fiber positioners (RFPs), is the one with the highest spectra acquisition rates. To guarantee no blind area, RFPs’ working spaces are overlapped to a certain extent, leading to collisions between RFPs and damage to RFPs. Even with algorithms designed for collision avoidance, collisions still occur during operation. Despite a 99.6% success rate of the current adopted path-planning algorithm, 4% of RFPs fail to reach targets. Fail reasons, such as collisions, cause ongoing negative effects across multiple observation rounds, necessitating the replacement of many RFPs. LAMOST is upgrading its fiber positioning system. Considering the above-mentioned problem in the design phase is necessary. To address this challenge, we propose a mathematical model to assess the collision probability. Then, the proposed model is validated by Monte Carlo simulations. During collision probability calculation, we consider factors such as RFP structure, target allocation, motion requirements, and mechanical errors into consideration. Based on this, we employ the genetic algorithm to optimize RFP arrangements with the lowest collision probability and show its function in the design phase. The proposed method is designed for LAMOST, but it is suitable for the future design of newly proposed spectroscopic telescopes with RFPs.