In the original Art Gallery Problem (AGP), one seeks the minimum number of
guards required to cover a polygon P. We consider the Chromatic AGP (CAGP),
where the guards are colored. As long as P is completely covered, the number
of guards does not matter, but guards with overlapping visibility regions must
have different colors. This problem has applications in landmark-based mobile
robot navigation: Guards are landmarks, which have to be distinguishable (hence
the colors), and are used to encode motion primitives, \eg, "move towards the
red landmark". Let χG(P), the chromatic number of P, denote the minimum
number of colors required to color any guard cover of P. We show that
determining, whether χG(P)≤k is \NP-hard for all k≥2. Keeping
the number of colors minimal is of great interest for robot navigation, because
less types of landmarks lead to cheaper and more reliable recognition