Control allocation of an arbitrary fully actuated multirotor aerial vehicle equipped with 1-DOF vectoring rotors

Resumo

The present paper deals with the control allocation of fully actuated multirotor aerial vehicles (MAVs) equipped with an arbitrary number of only radially vectoring rotors. To tackle the problem, we first consider a control architecture in which the control allocator is cascaded with the control laws. Therefore, the latter provides the resultant force-torque commands for the former to distribute them among the available actuators, which include the spinning and the vectoring motors. We formulate the control allocator through an optimization problem in which the rotor thrust vectors represented in body-fixed frames are the design variables. In this way, the control allocation equation becomes linear since it does not explicitly include the commands for the vectoring angles, which can be immediately computed afterwards using the computed optimal thrust vectors. In the optimization problem, the thrust vectors are constrained in such a way to respect given bounds on their magnitude and vectoring angle. It is noteworthy that, considering a minimal thrust magnitude, in general, greater than zero, the thrust vectors span non-convex sets, thus making the original problem a non-convex optimization. However, instead of dealing with such convex sets, we have replaced them by convex ones, thus given rise to a convex program that approximates the original problem. The method is widely evaluated by computer simulations on a hexa-rotor with all the six rotors equipped with a one-degree-of-freedom vectoring mechanism.