  As fully-actuated systems, omnidirectional multirotor aerial vehicles (OMAVs)
have more flexible maneuverability and advantages in aggressive flight in
cluttered environments than traditional underactuated MAVs. %Due to the high
dimensionality of configuration space, making the designed trajectory
generation algorithm efficient is challenging. This paper aims to achieve safe
flight of OMAVs in cluttered environments. Considering existing static
obstacles, an efficient optimization-based framework is proposed to generate
6-D $SE(3)$ trajectories for OMAVs. Given the kinodynamic constraints and the
3D collision-free region represented by a series of intersecting convex
polyhedra, the proposed method finally generates a safe and dynamically
feasible 6-D trajectory. First, we parameterize the vehicle's attitude into a
free 3D vector using stereographic projection to eliminate the constraints
inherent in the $SO(3)$ manifold, while the complete $SE(3)$ trajectory is
represented as a 6-D polynomial in time without inherent constraints. The
vehicle's shape is modeled as a cuboid attached to the body frame to achieve
whole-body collision evaluation. Then, we formulate the origin trajectory
generation problem as a constrained optimization problem. The original
constrained problem is finally transformed into an unconstrained one that can
be solved efficiently. To verify the proposed framework's performance,
simulations and real-world experiments based on a tilt-rotor hexarotor aerial
vehicle are carried out.
