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This paper presents a complete characterization of shortest paths to a goal position for a robot with unicycle kinematics and an on-board camera with limited field-of-view (FOV), which must keep a given feature in sight. Previous work on this subject has shown that the search for a shortest path can be limited to simple families of trajectories. In this paper, we provide a complete optimal synthesis for the problem, i.e., a language of optimal control words, and a global partition of the motion plane induced by shortest paths, such that a word in the optimal language is univocally associated with a region and completely describes the shortest path from any starting point in that region to the goal point. An efficient algorithm to determine the region in which the robot is at any time is also provided.