Lyapunov-based Hierarchical Control Design of a Quad-Rotorcraft with Singularity Avoidance

Abstract

A hierarchical framework is proposed for tracking control of a quad-rotorcraft. A nonlinear position controller commands the required thrust to move the vehicle along the reference trajectory while a nonlinear attitude controller computes the torque to achieve the desired orientation. The underlying principle behind hierarchical control is to design a thrust input such that the vehicle tracks the desired position and compute guided attitude from the thrust input so that designed rotor torques drives the vehicle orientation to the desired one. A strategically designed smooth position controller facilitates singularity-free attitude reference extraction and therefore, attitude tracking is achieved without singularity. A rigorous stability analysis proves that the overall closed-loop system is asymptotically stable (AS). The hierarchical control design is based on full state space Euler-Lagrange (E-L) model of a quad-rotorcraft. Unlike Newton-Euler (N-E) dynamics where desired attitude is reached using vehicle angular velocity as an intermediate control, the design exploits E-L dynamics to track the desired attitude using computed torque control. Numerical simulation shows the performance of the proposed controller.