Real-time Collision-free Motion Planning for Next-generation Fiber Positioners in LAMOST

Abstract Multiobject fiber-fed spectrographs have thousands of fiber positioners packed on a focal plane with shared working space to move the fiber-ends in parallel, which maximizes observation time. In order to further improve the spectrum acquiring rate, the second stage of LAMOST is pursuing miniaturization and high density of fiber positioners. However, their smaller size and increased density introduce greater challenges in positioning and replacement, which necessitate more advanced anticollision measures to ensure smooth operation. In this study, we first present a real-time control strategy that makes trajectory of positioner predictable and then propose a real-time collision-free motion-planning algorithm. We classify collisions based on predicted trajectories and obtain collision-free paths. One of the fiber positioners in each collision pair is selected as waiting robot, retracting robot or extending robot. Under real-time control, positioners will move along the collision-free paths. Simulations validated that the success rate in avoiding collisions of the proposed method increased from 98.96% to 100%. A prototype measurement platform was set up to verify the scientific validity of our algorithm, and the results have shown that all 6300 fiber positioners could avoid collisions. As the trajectory of a positioner can be divided into no more than six parts, collisions among thousands of positioners can be divided into many collision pairs. Thus, our algorithm can be used in other instruments with equal-arm theta-phi positioners.