An application of Non-Linear Model Predictive Control (NLMPC) to the stabilisation of a kinematic model of a two wheel mobile robot with input and (non-holonomic) state constraints is studied. Since linear (and even successively linearised or time-variant) MPC is not feasible for this mechanical benchmark problem (as the linearisation around any fixed point is not controllable and the assumptions for guaranteed stability with stability constraints fail), the potential of non-linear predictive control techniques is investigated. The NLMPC implementation is discussed and results are presented for several configurations. The expense and reliability of the non-convex optimisation causes problems. Tuning of the controller parameters appears to be decisive. In general, terminal state constraints are required to guarantee asymptotical stability. In this paper, these constraints are, analogous to the linear case, replaced by time-varying (exponential) weightings which are easier to handle. The results for the newly proposed non-linear control scheme are very promising, including improved convergence rates. The advantages of predictive control (constraint handling) are fully exploited. Still, the excessive computational demands make real-time implementation almost impossible and stability and robustness issues need to be further investigated.