Astronomy & Astrophysics manuscript no. aa c ESO 2013 December 6, 2013 Collision Avoidance in Next-generation Fiber Positioner Robotic System for Large Survey Spectrograph Laleh Makarem 1, 7 , Jean-Paul Kneib 2, 3 , Denis Gillet 1 , Hannes Bleuler 4 , Mohamed Bouri 4 , Laurent Jenni 4 , Francisco Prada 5, 6 , and Justo Sanchez 5 1 Coordination and Interaction Systems Group (REACT), Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland 2 Laboratory of Astrophysics (LASTRO), Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, Ch-1290 Versoix, Switzerland 3 Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388, Marseille, France 4 Laboratory of Robotic Systems (LSRO) Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland 5 Instituto de Astrofisica de Andalucia (CSIC), Granada, E-18008, Spain 6 Instituto de Física Teórica, (UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, E-28049 Madrid, Spain 7 e-mail: laleh.makarem@epfl.ch December 6, 2013 ABSTRACT Some of the next generation massive spectroscopic survey projects, such as DESI and PFS, plan to use thousands of fiber positioner robots packed at a focal plane to quickly move in parallel the fiber-ends from the previous to the next target points. The most direct trajectories are prone to collision that could damage the robots and impact the survey operation. We thus present here a motion planning method based on a novel decentralized navigation function for collision-free coordination of fiber positioners. The navigation function takes into account the configuration of positioners as well as the actuator constraints. We provide details for the proof of convergence and collision avoidance. Decentralization results in linear complexity for the motion planning as well as dependency of motion duration with respect to the number of positioners. Therefore the coordination method is scalable for large-scale spectrograph robots. The short in-motion duration of positioner robots (∼2.5 seconds using typical actuator constraints), will thus allow the time dedicated for observation to be maximized. Key words. astronomical instrumentation, methods and techniques; instrumentation: spectrographs; surveys; collision avoidance; motion control; multi agent robotics; collective motion planning; decentralized navigation function 1. Introduction After the discovery and confirmation of the accelerated expan- sion of the universe (Riess et al. 1998; Perlmutter et al. 1999), one of the main challenges in cosmology is to discern the nature of the dark energy. In order to achieve this goal, different obser- vational techniques have been proposed to tackle the geometry and evolution of the Universe. One of the key techniques is the measurement of the Baryonic Acoustic Oscillations (BAO) in massive spectroscopic surveys. The very first large-scale spectroscopic survey (Huchra et al. 1983) revealed a cosmic web structure with filaments and voids, and soon after, further investigations questioned the existence of a cosmological constant (Efstathiou et al. 1990). More re- cently, following the discovery of the imprint of the BAO in the Sloan Digital Sky Survey (SDSS; Eisenstein et al. 2005), massive spectroscopic surveys have been developed to measure accurately the evolution of the distance-redshift relation using the BAO technique. In particular, 1) the WiggleZ redshift survey (Blake et al. 2011) has completed a ∼250,000 redshift survey of star-forming galaxies (at z < 0.8) at the 4m Anglo Australian Telescope (AAT), 2) the Baryonic Oscillation Spectroscopic Sur- vey (BOSS; Anderson et al. 2012) will complete in 2014 a major redshift survey of 1.4 million galaxy redshift (at z < 0.7) and 160,000 high-redshift Lyman-α quasars using the SDSS tele- scope, and 3) the extended-BOSS survey (2014-2020) will com- plete the first BAO survey over the redshift range 0.7 < z < 2.2 using galaxies and quasars as well as the SDSS facility. To go beyond the throughput limits of current surveys, new technologies are being developed to fasten the future spectro- scopic facilities. The way forward is not only to use larger aperture telescopes, but also to use a larger multiplexing. Over the past few years two major projects have been approved for construction. First, the Primary Focus Spectrograph (PFS) is a Japanese lead project that aims to develop a 2400-fiber spectro- graph on the 8.2 m Subaru telescope. Second, the Dark Energy Spectroscopic Instrument (DESI) 1 , a DOE lead project, aims to develop a 5000-fiber spectrograph on the Mayall 4m telescope. Other less advanced projects are also being prepared such as 4MOST and WEAVE. Spectrographs fed by massive fiber bundles are one of the most advanced and proven methods compared with multi-slit approach. Various technologies have been proposed for fiber po- sitioning. For example, in the case of the SDSS spectrograph, fibers are placed manually into the holes drilled in an aluminum plate. This operation is done during the day time prior to obser- vations. In the case of the AAT spectrograph a robot is plac- ing a fiber after a fiber at the target point. This operation is done while another set of fiber is observing. In the case of the Chinese Large Sky Area Multi-Object Fibre Spectroscopic Tele- 1 http://desi.lbl.gov Article number, page 1 of 9 arXiv:1312.1644v1 [astro-ph.IM] 5 Dec 2013