Robust Variable-Horizon MPC for Landing a Multirotor UAV on a Moving Platform

Abstract: Landing a multirotor Unmanned Aerial Vehicle (UAV) on a moving platform is challenging because a UAV is underactuated and the desired landing state is generally a non-equilibrium state. Shrinking- and variable-horizon approaches are promising for reaching such non-equilibrium targets, but often lack robustness to disturbances. Robust Variable-Horizon Model Predictive Control (VH-MPC) addresses this limitation but is computationally complex for a high-dimensional system such as a multirotor UAV. This paper presents a computationally efficient robust Variable-Horizon MPC method for reaching non-equilibrium targets under bounded disturbances. The online horizon search is restricted to a neighborhood of the previously selected horizon, while maintaining recursive feasibility under bounded disturbances. A fixed robust positively invariant tube provides horizon-independent constraint tightening. By exploiting the differential flatness property of a UAV, this approach is applied to a decoupled linearized system, enabling real-time implementation on an onboard Raspberry Pi 5 at 20 Hz. Simulations show that restricting the horizon search substantially reduces computation with limited impact on the objective, while real-time Gazebo simulations demonstrate the robustness of the method. Physical experiments demonstrate successful landing of a multirotor UAV on a moving Stewart platform.