Tube-Based Explicit Model Predictive Control for a Tiltrotor UAV in Cargo Transportation Tasks

In this paper, we present a robust control strategy based on model predictive control (MPC) for a tiltrotor unmanned aerial vehicle in suspended load transportation tasks, from the perspective of the load. To this aim, we propose a new formulation of tube-based MPC for high-order dynamical systems, allowing its embedded implementation. The proposed formulation computes an explicit solution to the optimization problem using the nominal part of an uncertain linear parameter-varying (LPV) system, while a second control law is used to compensate for the differences between the nominal and uncertain models. To compute the feedback gain used by the second control law, we propose a novel group of LMIs based on the uncertain LPV model where the uncertainty set is represented as a zonotope. The reachable set, used in the MPC strategy, is computed as a robust positive invariant set also using zonotopes, reducing the computational cost and allowing its offline computation. Furthermore, by using the uncertain LPV model and the computed feedback gain, our reachable set algorithm not only guarantees the existence of nominal control and state sets, but also incorporates unmodeled uncertainties and external disturbances. This approach ensures robustness and minimizes the volume of the set. Additionally, we develop an algorithm based on parallel programming for fast computation of the control signal in a real-time implementation, which takes advantage of the explicit solution of the tube-based MPC formulation. Finally, numerical experiments are obtained to corroborate the proposed controller performance via a hardware-in-the-loop framework with a high-fidelity simulator developed on Gazebo and ROS. A detailed video of the results is available at youtu.be/UHPjN81y9hc.