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In this paper we present a tracking controller for a class of underactuated mechanical systems, based on a backstepping procedure. This class includes an approximation of small helicopter dynamics. The need to avoid artificial singularities due to the attitude representation is the main driver behind the control design presented in this paper: to achieve this goal, we will operate directly in the configuration manifold of the vehicle. The control design provides asymptotic tracking for an approximate model of small helicopters, and bounded tracking when more complete models are considered. Simulation examples, including both point stabilization and aggressive maneuver tracking, are presented and discussed.
Frazzoli et al. (Sat,) studied this question.