Gaussian Process Model Predictive Control of an Unmanned Quadrotor

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 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) algorithm and an existing constrained nonlinear GP based MPC algorithm. In the first comparison, 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 the second comparison, simulation results demonstrate that our approach only requires 20% of the computational time for the existing nonlinear GP based MPC.