A Survey on Methods for Elaborated Modeling of the Mechanics of a Small-Size Helicopter. Analysis and Comparison

Abstract

RED-UAS 2011 paper. When designing new control techniques for unmanned helicopters, the development of mathematical models that reproduce the dynamics of the real platform is a matter of importance. This allows the usage of model-based approaches that achieve better adaptation of the control laws to the real system. In these cases, the objective is not to obtain complex equations like those required for high-fidelity simulations. Instead, the aim is to derive simple and manageable models that ease the derivation of the control laws, maintaining at the same time their capability to reproduce the main behavior of the real system. The dynamics of a small-size helicopter with a stiff main rotor are mainly described by its mechanical model. Accordingly, this paper analyzes in detail three representative methods for elaborated modeling of the mechanics of small-size helicopters: Newton–Euler, Lagrange and Kane. For that purpose, the most general case is considered: two rigid bodies, fuselage and main rotor. As a consequence, the resulting models account for most significant modeling issues in the mechanical behavior of a small-size helicopter, such as the gyroscopic effect. Although the equations obtained using the three approaches are equivalent in the sense that they generate the same numerical results in simulation, Kane’s method holds some unique advantages.