In this paper, we solve the complete coordination problem of robotic fiber positioners using supervisory control theory. In particular, we model positioners and their behavioral specifications as discrete-event systems by the discretization of their motion spaces. We synthesize a coordination supervisor associated with a specific set of positioners. In particular, the coordination supervisor includes the solutions to the complete coordination problem of its corresponding positioners. Then, we use the backtracking forcibility technique of supervisory control theory to present an algorithm based on a completeness condition to solve the coordination problem similar to a reconfiguration problem. We illustrate the functionality of our method using an example.