  This paper presents an image-based visual servo control (IBVS) method for a
first-person-view (FPV) quadrotor to conduct aggressive aerial tracking. There
are three major challenges to maneuvering an underactuated vehicle using IBVS:
(i) finding a visual feature representation that is robust to large rotations
and is suited to be an optimization variable; (ii) keeping the target visible
without sacrificing the robot's agility; and (iii) compensating for the
rotational effects in the detected features. We propose a complete design
framework to address these problems. First, we employ a rotation on $SO(3)$ to
represent a spherical image feature on $S^{2}$ to gain singularity-free and
second-order differentiable properties. To ensure target visibility, we
formulate the IBVS as a nonlinear model predictive control (NMPC) problem with
three constraints taken into account: the robot's physical limits, target
visibility, and time-to-collision (TTC). Furthermore, we propose a novel
attitude-compensation scheme to enable formulating the visibility constraint in
the actual image plane instead of a virtual fix-orientation image plane. It
guarantees that the visibility constraint is valid under large rotations.
Extensive experimental results show that our method can track a fast-moving
target stably and aggressively without the aid of a localization system.
