Modeling and dynamical analysis of a small-scale unmanned helicopter

A simple model comprising five differential equations reflecting the attitude dynamics of small-scale hovering helicopters is developed. From its force analysis, this helicopter system has the dynamic structure of a Kolmogorov model producing chaos. The stable-focus mode and chaotic mode are identified for the helicopter. The hidden chaotic attraction basin is identified, which demonstrates the multi-stability of the helicopter and highly sensitivity with initial location. Varying the configuration of the moment of inertia leads to a change in dynamics for the helicopter system. The analysis of its chaotic motion is significant for designing of the controller as well as the configuration of parameters so as to avoid instabilities that produce chaos through improper assembly or selection of materials. The Lyapunov exponent spectra and the two-parameter bifurcation in terms of moment of inertia exhibit rich dynamical modes: stable, periodic orbit, pseudo-periodic orbit, and chaotic. A perturbation feedback control method is applied to control the system subjecting to chaos situation to reach the periodic orbit or equilibrium point. This control just needs a single controller but does not need the control input computation. The proposed model and the discovery of chaos provide a benchmark for the design and research of control algorithms for similar helicopter systems.