A fully-actuated quadcopter representation using quaternions

Recent advances in practical fields like robotics and the miniaturisation of many sensors and actuators have turned autonomous vehicles into a reality. These systems come in many shapes and forms depending on the medium and their design but can be classified in one of two categories according to their mechanical configuration and number of actuators: fully-actuated and under-actuated vehicles; the second group still poses many challenges for the automatic control and robotics communities. This work introduces an easy methodology, based on quaternions, for designing controllers for a class of under-actuated systems, such as multicopter vehicles. The methodology starts from a fully-actuated representation of the system and adapts it to be implemented in under-actuated systems. In addition, it allows the easy development of controllers without taking care the coupled dynamics of the system. The proposed approach is based on Lyapunov's stability theory and is proven for certain criteria of the system's dynamics. The quadcopter configuration is used to validate the proposed methodology in simulations and in experimental tests.