Generating 6-D Trajectories for Omnidirectional Multirotor Aerial Vehicles in Cluttered Environments

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.