Geometric Modeling and Controllability Analysis of a Quadrotor with a Suspended Load

Abstract

This paper addresses the modeling and controllability analysis for the hybrid multi-body systems of a quadrotor with a cable suspended load. According to the cable is stressed or not, two subsystems of this hybrid multi-body model are built on the nonlinear manifolds $\mathbb{R}^{3}\times \mathbb{R}^{3}\times SO(3)$ and $\mathbb{R}^{3}\times \mathbb{S}^{2}\times SO(3)$, respectively, which have simpler and more global expressions compared with those on local parameter presentations. And the switching characteristics between these two subsystems are considered. Moreover, it is verified that the subsystem with zero cable tension is uncontrollable and the subsystem with nonzero cable tension is linear locally controllable and small time local controllable (STLC) using linear and nonlinear theory, respectively