  The Model Predictive Control (MPC) trajectory tracking problem of an unmanned
quadrotor with input and output constraints is addressed. In this article, the
dynamic models of the quadrotor are obtained purely from operational data in
the form of probabilistic Gaussian Process (GP) models. This is different from
conventional models obtained through Newtonian analysis. A hierarchical control
scheme is used to handle the trajectory tracking problem with the translational
subsystem in the outer loop and the rotational subsystem in the inner loop.
Constrained GP based MPC are formulated separately for both subsystems. The
resulting MPC problems are typically nonlinear and non-convex. We derived 15 a
GP based local dynamical model that allows these optimization problems to be
relaxed to convex ones which can be efficiently solved with a simple active-set
algorithm. The performance of the proposed approach is compared with an
existing unconstrained Nonlinear Model Predictive Control (NMPC). Simulation
results show that the two approaches exhibit similar trajectory tracking
performance. However, our approach has the advantage of incorporating
constraints on the control inputs. In addition, our approach only requires 20%
of the computational time for NMPC.
