不同类型Theta-phi定位器碰撞概率的通用评估方法
General Methods for Evaluating Collision Probability of Different Types of Theta-phi Positioners
AI总结：
针对天文望远镜机器人光纤定位器的碰撞风险问题，研究提出碰撞概率数学模型与快速计算方法，可适配不同臂长的定位器，且泊松分布目标分配能平均降低约2.6%的碰撞概率。
摘要：
在许多现代天文设施中，多目标望远镜是关键仪器。这类望远镜的焦平面上大多安装了数千个机器人光纤定位器（RFP），它们共享重叠的工作空间。RFP在运动过程中发生碰撞会导致部分目标无法被观测，并造成结构损坏，因此有必要对RFP的碰撞概率进行合理的评估与测算。本研究提出了一种碰撞概率的数学模型，并通过蒙特卡洛模拟验证了模型结果的有效性。此外，本文还提出了一种新的碰撞计算方法以提升计算速度，耗时仅为原方法的约0.15%。模拟实验证实，该方法既能评估臂长相等的RFP间的碰撞概率，也适用于臂长不等的情况。研究还发现，采用基于泊松分布的目标分布方式可使碰撞概率平均降低约2.6%。
英文摘要：
In many modern astronomical facilities, multi-object telescopes are crucial instruments. Most of these telescopes have thousands of robotic fiber positioners(RFPs) installed on their focal plane, sharing an overlapping workspace. Collisions between RFPs during their movement can result in some targets becoming unreachable and cause structural damage. Therefore, it is necessary to reasonably assess and evaluate the collision probability of the RFPs. In this study, we propose a mathematical models of collision probability and validate its results using Monte Carlo simulations. In addition, a new collision calculation method is proposed for faster calculation(nearly 0.15% of original time). Simulation experiments have verified that our method can evaluate the collision probability between RFPs with both equal and unequal arm lengths. Additionally, we found that adopting a target distribution based on a Poisson distribution can reduce the collision probability by approximately 2.6% on average.
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