  Due to the nonlinearities and operational constraints typical to quadcopter
missions, Model Predictive Control (MPC) encounters the major challenge of high
computational power necessary for the online implementation. This problem may
prove impractical, especially for a hardware-limited or small-scale setup. By
removing the need for online solvers while keeping the constraint satisfaction
and optimality, Explicit MPC (ExMPC) stands out as a strong candidate for this
application. Yet, the formulation was usually hindered by the two main
problems: nonlinearity and dimensionality. In this paper, we propose an ExMPC
solution for the quadcopter position stabilization by analyzing its description
(dynamics and constraints) in the flat output space. With the former issue, the
system is exactly linearized into a concatenation of three double integrators
at a price of cumbersome constraints in the new coordinates. For the latter,
with a suitable characterization of these constraints, the stabilizing ExMPC
can be computed for each double integrator separately. The controller is then
validated via simulations and experimental tests. The proposed scheme achieves
similar performance and guarantees to the state-of-the-art solution but with
notably less computational effort, allowing scalability in a centralized manner
