  This paper presents a data-driven optimal control policy for a micro flapping
wing unmanned aerial vehicle. First, a set of optimal trajectories are computed
off-line based on a geometric formulation of dynamics that captures the
nonlinear coupling between the large angle flapping motion and the quasi-steady
aerodynamics. Then, it is transformed into a feedback control system according
to the framework of imitation learning. In particular, an additional constraint
is incorporated through the learning process to enhance the stability
properties of the resulting controlled dynamics. Compared with conventional
methods, the proposed constrained imitation learning eliminates the need to
generate additional optimal trajectories on-line, without sacrificing
stability. As such, the computational efficiency is substantially improved.
Furthermore, this establishes the first nonlinear control system that
stabilizes the coupled longitudinal and lateral dynamics of flapping wing
aerial vehicle without relying on averaging or linearization. These are
illustrated by numerical examples for a simulated model inspired by Monarch
butterflies.
