  Robots and automated systems are increasingly being introduced to unknown and
dynamic environments where they are required to handle disturbances, unmodeled
dynamics, and parametric uncertainties. Robust and adaptive control strategies
are required to achieve high performance in these dynamic environments. In this
paper, we propose a novel adaptive model predictive controller that combines
model predictive control (MPC) with an underlying $\mathcal{L}_1$ adaptive
controller to improve trajectory tracking of a system subject to unknown and
changing disturbances. The $\mathcal{L}_1$ adaptive controller forces the
system to behave in a predefined way, as specified by a reference model. A
higher-level model predictive controller then uses this reference model to
calculate the optimal reference input based on a cost function, while taking
into account input and state constraints. We focus on the experimental
validation of the proposed approach and demonstrate its effectiveness in
experiments on a quadrotor. We show that the proposed approach has a lower
trajectory tracking error compared to non-predictive, adaptive approaches and a
predictive, non-adaptive approach, even when external wind disturbances are
applied.
