  Mobility properties inside and around degenerate domains of an elastic
lattice partially pinned on a square array of traps are explored by means of a
fully controllable model system of macroscopic particles. We focus on the
different configurations obtained for filling ratios equal to 1 or 2 when the
pinning strength is lowered. These theoretically expected but never observed
configurations are degenerated, which implies the existence of a multidomain
crystal. We show that the distinction between trapped and untrapped particles
that is made in the case of strong pinning is not relevant for such a weaker
pinning. Indeed, one ought to distinguish between particles inside or around
the domains associated to positional degeneracies. The possible consequences on
the depinning dynamics of the lattice are discussed.
