The goal of this work is to investigate an approach to model predictive control in constrained settings, where the motion involves constraints and compliant motion is desired. Specifically, the fixed Lagrangian should be evaluated on a simulated two link serial robot model performing a motion that involves sliding. For this task, it is needed to setup a simulation environment for the modeled system, to implement the control strategy and to analyze this control strategy with respect to the stiffness along the planned trajectory. Further on, there will be a theoretical investigation of the closed-loop system regarding stability. As an advanced test scenario a position error in the sliding surface is introduced. Hence, only position control will fail, since either the system could be damaged due to a \emph{high-gain feedback} behavior or the contact and thus the sliding motion will not occur. Therefore, it is investigated whether it is possible to extend the control structure in order to ensure that the sliding motion takes place as desired.