Hybrid Optimal Control of a Flying+Sailing Drone

Abstract This paper studies the combined maneuver of flying and sailing for a robotic system which is referred to as a flying+sailing drone. Due to the emergence of hybrid systems behavior in tasks which involve both the flying and sailing modes, a hybrid systems formulation of the robotic system is presented. Key characteristics of the system are (i) changes in the dimension of the state space as the system switches from flying to sailing and vice versa and (ii) the presence of autonomous switchings triggered only upon the landing of the drone on the water surface. For the scenario in which the drone's initial state is given in the flying mode and a fixed terminal state is specified in the sailing mode, the associated optimal control problems are studied within the vertical plane passing through the given points, hence the dynamics of the drone in the flying mode are represented in a five-dimensional state space (associated with three degrees-of-freedom) and in a three-dimensional state space in the sailing mode (associated with two degrees-of-freedom). In particular, the optimal control problems for the minimization of time and the minimization of the control effort are formulated, the associated necessary optimality conditions are obtained from the Hybrid Minimum Principle (HMP), and the associated numerical simulations are presented.