Globally Attractive Hyperbolic Control for the Robust Flight of an Actively Tilting Quadrotor

Abstract

This paper addresses the problem of robustly controlling an actively tilting quadrotor UAV. The proposed technique is model-free and it is based on hyperbolic functions of the six-dimensional pose error of the UAV with respect to the world reference frame; this hyperbolic controller globally attracts the error signals to an ultimate bound about the origin despite external disturbances, which is proved by way of a strict Lyapunov function based analysis. The effectiveness of the controller is evaluated by means of tracking and regulation experiments on adverse conditions, which were implemented on a virtual model of the UAV through a physics-engine-based simulation environment that provides an almost identical behaviour than a real UAV. The norm of the six-dimensional error signal converged to zero for the regulation experiments, whereas for tracking it did not exceed 0.05 meters, which indicated a successful operation of the control system. In addition, the performance of the hyperbolic controller was contrasted against a nonlinear PID, which resulted in a better performance in favour of the first one, who settled the errors to zero up to eight seconds before and demanded up to 2000 less revolutions per minute from the rotors while performing the same regulation tasks. All the aforesaid successful results place the proposed technique as a competitive alternative for controlling actively tilting multirotors due to its simplicity, robustness and demonstrated effectiveness.