A Singularity-free Hierarchical Nonlinear Quad-Rotorcraft Control using Saturation and Barrier Lyapunov Function

A singularity-free nonlinear hierarchical control framework is proposed in this paper for control of a quad-rotorcraft unmanned aerial vehicle (UAV). A saturation control scheme with hyperbolic tangent function is designed for the position loop controller to ensure non-singular command attitude extraction and the effect of nonlinear coupling between the position and attitude subsystem is subsequently analyzed. The problem of sign-ambiguity commonly appears in reference attitude is overcome using arc tangent function by considering the signs of both the arguments. To obviate the problem of singularity during attitude tracking, a non-singular attitude loop controller using barrier Lyapunov function (BLF) with corresponding initial condition constraint is proposed. A rigorous stability analysis proves that the overall closed-loop system is asymptotically stable (AS) and all the signals are bounded in the cascaded control structure. The singularity-free hierarchical control development and its stability analysis exploits the full state space Euler-Lagrange under-actuated dynamics in terms of generalized coordinates with generalized force and torque collocated with generalized velocities. Simulation results show the performance of the proposed controller.