提出快速评估天文望远镜机械臂碰撞概率的新方法
General Methods for Evaluating Collision Probability of Different Types of Theta-phi Positioners
- 构建数学模型结合蒙特卡洛模拟评估碰撞概率
- 计算速度提升至原方法的约667倍（0.15%耗时）
- 适用于长短臂不一的机械臂，适合望远镜控制系统优化
在现代天文设施中，多目标望远镜依赖数千个安装在焦平面的机器人光纤定位器（RFPs），共享重叠工作区。运动过程中RFPs间碰撞可能导致目标无法触及并造成结构损伤。因此，合理评估碰撞概率至关重要。本文提出一种碰撞概率数学模型，并通过蒙特卡洛模拟验证其有效性。同时，提出一种新的快速碰撞计算方法，计算耗时仅为原方法的0.15%。仿真实验表明，该方法可有效评估等长与不等长臂长定位器间的碰撞概率。此外，采用泊松分布的目标分布可平均降低2.6%的碰撞概率。
原文摘要 · Abstract (English)
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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