This paper presents a geometric optimal controller for a fully-actuated hexrotor unmanned aerial vehicle (UAV). The aim of this research is to exploit a structural property, relation between the rotor thrust force and the vehicle acceleration, to improve the control performance. First, the system dynamics is expressed on the special Euclidean group SE(3). A geometric optimal control method based on geodesic distance on SE(3) is then provided and applied to the hexrotor UAV. The newly developed optimal control law allows to consider the structural property of the UAV in the cost function. It is finally shown that the minimum cost of the optimal control can be reduced by maximizing dynamic manipulability of the vehicle.
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