  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.
