  This paper proposes a method for analyzing a series of potential motions in a
coupling-tiltable aerial-aquatic quadrotor based on its nonlinear dynamics.
Some characteristics and constraints derived by this method are specified as
Singular Thrust Tilt Angles (STTAs), utilizing to generate motions including
planar motions. A switch-based control scheme addresses issues of control
direction uncertainty inherent to the mechanical structure by incorporating a
saturated Nussbaum function. A high-fidelity simulation environment
incorporating a comprehensive hydrodynamic model is built based on a
Hardware-In-The-Loop (HITL) setup with Gazebo and a flight control board. The
experiments validate the effectiveness of the absolute and quasi planar
motions, which cannot be achieved by conventional quadrotors, and demonstrate
stable performance when the pitch or roll angle is activated in the auxiliary
control channel.
