A Singularity-Free Robust Hierarchical Quad-Rotorcraft Control Exploiting First Order Drag Effects

Dynamic response and performance of a quad-rotorcraft is influenced mostly by first order drag-like effects over a wide envelope of operating conditions, however, they are hard to model. A robust controller is designed to achieve satisfactory tracking performance in the presence of drag effects considering them as nonlinear model uncertainties in the dynamics. Majority of the work on robust stabilization is for fully actuated attitude and altitude subsystem where the coupling between position and attitude systems is not considered rigorously using Lyapunov based stability analysis. Ensuring robust stability of the overall (position and attitude) underactuated system considering drag effects is a challenge. A popular strategy is to use first order sliding mode control to restrain first-order drag forces where the chattering effect, caused due to discontinuous control effort, is mitigated by adaptive sliding mode action. Robust high gain observers are used to estimate unknown perturbation that opposes the motion of the vehicle. Higher order sliding mode controller is designed to achieve asymptotic tracking without any observer or adaptive updates. Few works achieve robust stability and tracking by proposing a nominal controller for the overall system with a robust compensator. The proposed work is a hierarchical nonlinear robust control design that uses Euler-Lagrange (E-L) dynamics to compute guidance and control laws simultaneously. The underactuated E-L model considers generalized forces and torques along with drag force and torque models, which are non-smooth nonlinearities but norm-bounded. The position and attitude control laws are designed with matched and unmatched state dependent model uncertainties for the cascade system to ensure that the origin of the overall error dynamics is asymptotically converging to an ultimate bound. Using Lyapunov analysis sufficient gain conditions are strategically derived to ensure stability. The size of the ultimate bound can be arbitrarily reduced by control system parameters.