A switching composition of horizontal and vertical controllers for a UAV to reach a 3D waypoint

The aim of this paper is to explore potential of feedback control design based on a switching composition of two controllers. The paper considers two stochastic optimal controllers for the motion of an unmanned aerial vehicle (UAV) in the horizontal and vertical planes. We show that the two controllers, one for reaching a point in the horizontal plane and the other for reaching and keeping a desired altitude in the vertical plane, can be computed using Cartesian coordinates. To reach a desired waypoint in 3D, both controllers are necessary while the vehicle has to reach simultaneously the horizontal and vertical navigation goals. For this reason, we compute the expected time of each controller toward its goal in 2D. Then, we propose a switching rule that guarantees the simultaneous arrival of each controller to its 2D goal, which is equivalent to the vehicle reaching the 3D waypoint. Finally, we explore a possibility for improvements of the switching rule using reinforcement learning and an actor-critic neural network. The paper results are illustrated by numerical simulations.