The Calibration of theta-phi Fiber Positioners Based on the Differential Evolution Algorithm

Abstract

Robotic fiber positioner (RFP) arrays are commonly adopted in multiobject spectroscopic instruments. The positioning accuracy is a common but vital issue for RFP as inaccurate fiber placement may heavily affect the observation performance. The calibration of RFP can effectively improve the positioning accuracy. Least-square is a widely used calibration method. However, it has disadvantages, such as sensitivity to the initial values and calculation complexity. To improve the positioning accuracy and reduce the iteration moves, we propose a new calibration method based on the differential evolution algorithm and verify it by calibrating the RFP of the Large Sky Area Multi-Object Fiber Spectroscopy Telescope. We first build the kinematic models of the RFP based on the Denavit–Hartenberg matrix and geometry relationship. Then, we analyze the error components and present the proposed calibration algorithms. The experiments are done with the digital universal tool microscope 19JC and the errors are calculated using the distance between the positions of achieved and target. Results show that the proposed algorithm can achieve higher accuracy than the least-square method and the average positioning accuracy is improved by 78.94% after calibration. Combined with the “pulse reduction” strategy and close-loop compensation, after two moves, the positioners can place the fiber ends within 40 μm of the intended location. The proposed calibration method is also suitable for other similar theta-phi positioners.