Priority coordination of fiber positioners in multi-objects spectrographs

Projects such as "The Dark Energy Spectroscopic Instrument" (DESI) [1] or "The Multi Object Optical and Near-infrared Spectrograph" (MOONS) [5] are developing spectrographs, composed of more than thousand of optical fibers in a confined hexagonal focal plane, to study the evolution of the universe. Such systems allow fast reconfiguration of the fibers as they are moved simultaneously to their assigned target by a 2-arm positioner within an short interval of time. Moreover, astronomers prioritize the observation of some objects over those that hold less information, creating a hierarchy of importances or priorities. In a scenario where not all the positioners can reach their targets, It is important to ensure the observation of the high-priority targets. In previous works, a decentralized navigation function from the family of potential fields was used for collision free coordination. While it guarantees convergence of all the positioners to their targets for DESI [1,2], it fails at planning motion for positioners in MOONS [3]. The reason is that the second arm of the positioners in MOONS is two times the length of the first arm. Covering a larger working space, they are prone to deadlocks, a situation where two or more positioners are blocked by each other and so unable to reach their targets. In this paper and in the framework of MOONS project, we present our new approach to integrate assigned priorities with the decentralized navigation functions to reduce the deadlocks situations. For this purpose, we regulate the movements of the positioners using a finite-state machine combined with distance-based heuristics. Each positioner's state dictates its behaviors with respect to other positioners. Distance-based heuristics limit the states transition when a positioner is interacting with its adjacent positioners to localize possible deadlock situations. The advantage of this method is its simplicity as it relies on local interaction of positioners, keeping the complexity of the algorithm quasilinear. In addition, since it does not depend on the positioner's geometry, it is also scalable to other positioner kinematics. We developed a motion planning simulator with a graphic interface in python to validate the coordination of the positioners with assigned priorities. As a result, the number of positioners converging to their targets improve from 60-70% to 80-95%. The computation time of the trajectories increases slightly due to the new layer of algorithm added for deadlocks prevention.