  The need for fully autonomous mobile robots has surged over the past decade,
with the imperative of ensuring safe navigation in a dynamic setting emerging
as a primary challenge impeding advancements in this domain. In this paper, a
Safety Critical Model Predictive Control based on Dynamic Feedback
Linearization tailored to the application of differential drive robots with two
wheels is proposed to generate control signals that result in obstacle-free
paths. A barrier function introduces a safety constraint to the optimization
problem of the Model Predictive Control (MPC) to prevent collisions. Due to the
intrinsic nonlinearities of the differential drive robots, computational
complexity while implementing a Nonlinear Model Predictive Control (NMPC)
arises. To facilitate the real-time implementation of the optimization problem
and to accommodate the underactuated nature of the robot, a combination of
Linear Model Predictive Control (LMPC) and Dynamic Feedback Linearization (DFL)
is proposed. The MPC problem is formulated on a linear equivalent model of the
differential drive robot rendered by the DFL controller. The analysis of the
closed-loop stability and recursive feasibility of the proposed control design
is discussed. Numerical experiments illustrate the robustness and effectiveness
of the proposed control synthesis in avoiding obstacles with respect to the
benchmark of using Euclidean distance constraints. Keywords: Model Predictive
Control, MPC, Autonomous Ground Vehicles, Nonlinearity, Dynamic Feedback
Linearization, Optimal Control, Differential Robots.
