In order to increase the workspace size of parallel robots (largely reduced by the presence of singularities) several solutions have been proposed. One promising solution consists in the definition of optimal trajectories that ensure the non degeneracy of the dynamic model in the singularity and therefore are able to cross the Type 2 singularities. Those works are based on the computation of the optimal trajectories and assume that the robot can perfectly track the desired trajectory. Nevertheless, this assumption cannot be verified in reality due to modelling errors which largely impact the control law used to follow the desired trajectory. Therefore, if the optimal trajectory is not perfectly tracked, the dynamic model can degenerate near the Type 2 singularities and the robot might stay blocked. In order to solve that problem, this paper proposes a multi-model approach that allows parallel robots to cross the Type 2 singularities without any torque discontinuity. The main idea is to shift near singularities from the full robot dynamic model to another simplified one that can never degenerate. The proposed control law is then coupled with an optimal trajectory planning methodology that makes the singularity crossing more robust to modelling errors. The proposed approach is validated experimentally on a prototype of Five-bar planar parallel mechanism.