Hybrid Optimal Control of a Flying+Sailing Drone: Flying with 6 and Sailing with 5 Degrees of Freedom

Abstract

This paper studies a multi-modal robotic system referred to as a flying+sailing drone with the consideration of six degrees of freedom (6-DoF) for flying and 5-DoF for sailing, i.e., a twelve-dimensional state space for flying and a ten-dimensional state space for sailing. Key characteristics of hybrid systems emerging in tasks involving both flying and sailing are (i) changes in the dimension of the state space as the system switches from flying to sailing and vice versa, (ii) the presence of autonomous switchings triggered upon the landing of the drone on the water surface, and (iii) non-identity jumps in the state upon switching. For the scenario in which the drone’s initial state is in the flying mode and a fixed terminal state is specified in the sailing mode, the associated optimal control problems are studied for the minimization of time and the minimization of the control effort. The necessary optimality conditions are obtained from the Hybrid Minimum Principle (HMP), and the associated numerical simulations are presented.