Dynamics of omni-directional multi-rotor aerial vehicles, hexacopter as a case study

This article presents a general formulation for the mathematical modeling of a specific class of aerial robots known as hexacopters. The mentioned robotic system, which consists of six arms with motors attached to each end, possesses a unique feature: it uses the minimum actuator required to reach a specific position in space with a defined orientation. To achieve this, it is vital to install the motors with an appropriate arrangement positioned at the end of each arm to ensure the robot's controllability. On the other hand, two virtual arms with zero lengths were used to describe the robot's orientation with regard to the inertial coordinate system in a tangible manner. One of the innovations carried out in this article is the standardization of the derivation of the motion equations of this robotic system procedure. For this purpose, first, the platform of the hexacopter is separated into several substructures. Following the previous step, the dynamic equations of each of these infrastructures are extracted in explicit form accordingly. Finally, the symbolic equations are merged, and as a result, the dynamic behavior of this aerial robot is formulated. The focus of this research is mainly on hexacopters. However, the presented method is generic enough to cover all aerial robots of this kind (with any number of arms and any relative arrangement between the members). Lastly, to show the robot's ability to reach a specific position in space with the desired orientation, the results of tracking a relatively complex trajectory by utilizing this robotic system are presented.