  This paper deals with the problem of time-constrained navigation of a robot
modeled by uncertain nonlinear non-affine dynamics in a bounded workspace of
$\mathbb{R}^n$. Initially, we provide a novel class of robust feedback
controllers that drive the robot between Regions of Interest (RoI) of the
workspace. The control laws consists of two parts: an on-line controller which
is the outcome of a Finite Horizon Optimal Control Problem (FHOCP); and a
backstepping feedback law which is tuned off-line and guarantees that the real
trajectory always remains in a bounded hyper-tube centered along the nominal
trajectory of the robot. The proposed controller falls within the so-called
tube-based Nonlinear Model Predictive control (NMPC) methodology. Then, given a
desired high-level specification for the robot in Metric Interval Temporal
Logic (MITL), by utilizing the aforementioned controllers, a framework that
provably guarantees the satisfaction of the formula is provided. The proposed
framework can handle the rich expressiveness of MITL in both safety and
reachability specifications. Finally, the proposed framework is validated by
numerical simulations.
