  In this work, we propose a cascaded scheme of linear Model prediction Control
(MPC) based on Control Barrier Functions (CBF) with Dynamic Feedback
Linearization (DFL) for Vertical Take-off and Landing (VTOL) Unmanned Aerial
Vehicles (UAVs). CBF is a tool that allows enforcement of forward invariance of
a set using Lyapunov-like functions to ensure safety. The First control
synthesis that employed CBF was based on Quadratic Program (QP) that modifies
the existing controller to satisfy the safety requirements. However, the
CBF-QP-based controllers leading to longer detours and undesirable transient
performance. Recent contributions utilize the framework of MPC benefiting from
the prediction capabilities and constraints imposed on the state and control
inputs. Due to the intrinsic nonlinearities of the dynamics of robotics
systems, all the existing MPC-CBF solutions rely on nonlinear MPC formulations
or operate on less accurate linear models. In contrast, our novel solution
unlocks the benefits of linear MPC-CBF while considering the full underactuated
dynamics without any linear approximations. The cascaded scheme converts the
problem of safe VTOL-UAV navigation to a Quadratic Constraint Quadratic
Programming (QCQP) problem solved efficiently by off-the-shelf solvers. The
closed-loop stability and recursive feasibility is proved along with numerical
simulations showing the effective and robust solutions. Keywords: Unmanned
Aerial Vehicles, Vertical Take-off and Landing, Model Predictive Control, MPC,
Nonlinearity, Dynamic Feedback Linearization, Optimal Control.
