Energy-Efficient Trajectory Generation for a Hexarotor with Dual-Tilting Propellers

In this paper, we consider a non-conventional hexarotor whose propellers can be simultaneously tilted about two orthogonal axes: in this way, its underactuation degree can be easily adapted to the task at hand. For a given tilt profile, the minimum-energy trajectory between two prescribed boundary states is explicitly determined by solving an optimal control problem with respect to the angular accelerations of the six brushless motors. We also perform, for the first time, a systematic study of the singularities of the control allocation matrix of the hexarotor, showing the presence of subtle singular configurations that should be carefully avoided in the design phase. Numerical experiments conducted with the FAST-Hex platform illustrate the theory and delineate the pros and cons of dual-tilting paradigm in terms of maneuverability and energy efficiency.