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

Abstract

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