This paper proposes a joint optimization scheme of the structural design and control of a fully-actuated hexrotor unmanned aerial vehicle.The hexrotor dynamics is formulated on the special Euclidean group SE(3) which represents the position and attitude of a rigid body. An optimal control problem on SE(3) is then considered, and the optimal input and the associated viscosity solution of the Hamilton-Jacobi-Bellman equation are presented analytically. The solution, value function, expresses the minimum value of the cost function for a given initial state. The analytical form of the value function is then regarded as a function of structural variables, and the function is minimized by modifying the vehicle structure. A numerical example shows that the optimally-controlled optimal structure maximizes its dynamic manipulability measure. Moreover, the resulting structure and control system are shown to be energy-efficient.
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