On the control allocation of fully actuated multirotor aerial vehicles

Abstract

The present work deals with the optimal control allocation of fully actuated multirotor aerial vehicles (MAVs) equipped with fixed (non-vectoring and constant-pitch) rotors. To tackle the problem, a cascaded control architecture is considered in which the control allocation is separated from the control law itself. The latter provides the resulting control efforts (three-dimensional force and torque) from the desired state trajectory, while the former is entrusted to distribute the resulting control efforts among the available actuators. The control allocation is formulated as a convex optimization problem, which, on the one hand, unifies the previous methods and, on the other hand, extends the literature by rigorously considering the rotors' dynamics and bounds, thus resulting in a novel constrained optimal control allocation algorithm suitable for quite general fixed-rotor fully actuated MAVs. Moreover, a control-allocation feasibility analysis based on the control allocator admissible set is presented. It provides a necessary and sufficient condition for the existence of a solution to the control allocation problem. We argue that this condition can be explicitly used in the design of the control law, thus improving its synergy with the control allocator. The proposed control allocation method is mathematically analyzed and widely illustrated by the computer simulation of two non-planar omnidirectional MAVs.