This paper presents the application of several advanced control techniques to a nonlinear strongly coupled multivariable robot. The main difficulties come from the flexibility of the mechanical chain, but also from the lack of joints sensors. In a first stage, a state-feedback linear quadratic (LQG) technique and a model predictive control (MPC) are designed using optimal observers. Considering additional sensors that provide measurements of accelerations increases the robustness of the controlled system. The second stage consists into adding a supplementary robustness layer (i.e. explicitly considering the robust stability under unstructured uncertainties) on the stabilizing MPC developed at the previous stage. Comparative results are proposed highlighting the trade-off between robust stability and nominal performance for disturbances rejection.