  New quadrotor UAV control algorithms are developed, based on nonlinear
surfaces composed of tracking errors that evolve directly on the nonlinear
configuration manifold, thus inherently including in the control design the
nonlinear characteristics of the SE(3) configuration space. In particular,
geometric surface-based controllers are developed and are shown, through
rigorous stability proofs, to have desirable almost global closed loop
properties. For the first time in regards to the geometric literature, a region
of attraction independent of the position error is identified and its effects
are analyzed. The effectiveness of the proposed "surface based" controllers are
illustrated by simulations of aggressive maneuvers in the presence of
disturbances and motor saturation.
