Globally Defined Dynamic Modelling and Geometric Tracking Controller Design for Aerial Manipulator

This study presents a globally defined dynamics for a conventional multirotor equipped with a single $n\mathbf{-DOF}$ manipulator using modified Lagrangian dynamics. This enables the reformulation of entire dynamics directly on $\text{SO}(3)$ without exploiting any local coordinates, and thus problems such as the singularity of Euler angles can be avoided. Since skew-symmetric property of Coriolis matrix $C$ and inertia matrix facilitates stability analysis, we propose a method to compute $C$ which guarantees the skew-symmetric property by considering $C$ as a summation of two sub-matrices. Then, a geometric tracking controller is designed based on decoupled dynamics applying passive decomposition. The proposed controller guarantees almost global region of attraction. We validate our method via consecutive aerial flipping experiments.