Exploring a New Design Paradigm for Omnidirectional MAVs for Minimal Actuation and Internal Force Elimination: Theoretical Framework and Control

This paper presents a novel concept for achieving omnidirectionality in a multirotor aerial vehicle (MAV) that uses only 6 inputs and ensures no internal forces at the equilibria. The concept integrates a single actively-tilting propeller along with 3 pendulum-like links, each carrying a propeller, connected by passive universal joints to the main body. We show that this design ensures omnidirectionality while minimizing the internal forces and without resorting to overactuation (i.e., more than 6 inputs). A detailed dynamic model of the multi-link MAV is first developed. Afterwards, the analysis identifies the equilibrium configurations and illustrates that a forced equilibrium exists for every pose of the MAV's main platform. In order to render this equilibrium asymptotically stable for the closed-loop system, a geometric nonlinear controller is constructed using dynamic feedback linearization and backstepping techniques with the main platform configuration error being the left-trivialized error on SE(3). The stability of the closed-loop system is then investigated by employing standard Lyapunov arguments on the zero dynamics. We conclude by providing numerical simulations validating the proposed approach. They demonstrate the MAV capability to perform decoupled attitude and translational motions under non-zero initial conditions, parametric uncertainty, and actuators noise.