  In this paper we consider the problem of steering a state and input
constrained differential drive robot to a desired position and orientation
using model-predictive control (MPC). The viability kernel of the system is
determined using the theory of barriers. Moreover, local asymptotic stability
of the origin under the MPC closed-loop solution without stabilizing conditions
is shown. We then present numerical experiments to examine the dependency of
the required prediction horizon length in MPC near the origin, as well as at
parts of the kernel's boundary. It is found that the horizon increases as
initial conditions approach the boundary and, in particular, non-differentiable
parts of the boundary.
