  Understanding the drift motion and dynamical locking of crystalline clusters
on patterned substrates is important for the diffusion and manipulation of
nano- and micro-scale objects on surfaces. In a previous work, we studied the
orientational and directional locking of colloidal two-dimensional clusters
with triangular structure driven across a triangular substrate lattice. Here we
show with experiments and simulations that such locking features arise for
clusters with arbitrary lattice structure sliding across arbitrary regular
substrates. Similar to triangular-triangular contacts, orientational and
directional locking are strongly correlated via the real- and reciprocal-space
moir\'e patterns of the contacting surfaces. Due to the different symmetries of
the surfaces in contact, however the relation between the locking orientation
and the locking direction becomes more complicated compared to interfaces
composed of identical lattice symmetries. We provide a generalized formalism
which describes the relation between the locking orientation and locking
direction with arbitrary lattice symmetries.
