  This paper presents a dynamic model and a control system for a flapping-wing
unmanned aerial vehicle. Inspired by flight characteristics captured from live
Monarch butterflies, a new dynamic model is presented to account the effects of
low-frequency flapping and abdomen undulation. We developed it according to
Lagrangian mechanics on a Lie group to obtain an elegant, global formulation of
dynamics. Then, a feedback control system is presented to asymptotically
stabilize periodic motions with active motion of abdomen, and its stability is
verified according to Floquet theory. In particular, it is illustrated that the
abdomen undulation has the desirable effects of reducing the variation of the
total energy and also improving the stability of the proposed control system.
