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

Byeongjun Kim, Dongjae Lee, Jeonghyun Byun, H. Jin Kim

Abstract: This study presents a globally defined dynamics for a conventional multirotor equipped with a single <tex>$n\mathbf{-DOF}$</tex> manipulator using modified Lagrangian dynamics. This enables the reformulation of entire dynamics directly on <tex>$\text{SO}(3)$</tex> 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 <tex>$C$</tex> and inertia matrix facilitates stability analysis, we propose a method to compute <tex>$C$</tex> which guarantees the skew-symmetric property by considering <tex>$C$</tex> 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.