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A control approach is proposed for a class of underactuated vehicles in order to stabilize reference trajectories either in thrust direction, velocity, or position. The basic modeling assumption is that the vehicle is pro-pulsed via a thrust force along a single body-fixed direction and that it has full torque actuation for attitude control (i.e., a typical actuation structure for aircrafts, vertical take-off and landing (VTOL) vehicles, submarines, etc.). Additional assumptions on the external forces applied to the vehicle are also introduced for the sake of control design and stability analyses. They are best satisfied for vehicles which are subjected to an external force field (e.g., gravity) and whose shape induces lift forces with limited amplitude, unlike airplanes but as in the case of many VTOL drones. The interactions of the vehicle with the surrounding fluid are often difficult to model precisely whereas they may significantly influence and perturb its motion. By using a standard Lyapunov-based approach, novel nonlinear feedback control laws are proposed to compensate for modeling errors and perform robustly against such perturbations. Simulation results illustrating these properties on a realistic model of a VTOL drone subjected to wind gusts are reported.
Hua et al. (Tue,) studied this question.