  The planar bistable device [Tsakonas \textit{et al., Appl. Phys. Lett.},
2007, {\textbf{90}}, 111913] is known to have two distinct classes of stable
equilibria: the diagonal and rotated solutions. We model this device within the
two-dimensional Landau-de Gennes theory, with a surface potential and without
any external fields. We systematically compute a special class of transition
pathways, referred to as minimum energy pathways, between the stable equilibria
that provide new information about how the equilibria are connected in the
Landau-de Gennes free energy landscape. These transition pathways exhibit an
intermediate transition state, which is a saddle point of the Landau-de Gennes
free energy. We numerically compute the structural details of the transition
states, the optimal transition pathways and the free energy barriers between
the equilibria, as a function of the surface anchoring strength. For strong
anchoring, the transition pathways are mediated by defects whereas we get
defect-free transition pathways for moderate and weak anchoring. In the weak
anchoring limit, we recover a cusp catastrophe situation for which the rotated
state acts as a transition state connecting two different diagonal states.
