Astrobots are robotic manipulators present in the latest generation telescopes. Their role is to coordinate optical fibers in specific positions of a focal plane, so that it is possible to get astronomical information of a desired observation. The crowded arrangement of these manipulators inside the focal plane of a telescopes makes the coordination process so much complicated that it is not always possible for a single astrobot to reach its target configuration. Therefore the convergence verification before the execution of a coordination is of particular interest. However a formal method for this purpose has not yet been found in the past.