Motion Planning and Control of an Underactuated 3DOF Helicopter

We consider trajectory planning for an underactuated 3DOF helicopter, using the virtual holonomic constraint approach. First we choose constraint functions that describe the configuration variables along a desired motion in terms of some independent parametrization variable. This lets us describe the closed-loop system by some reduced order dynamics, the solution of which gives a feasible trajectory for the desired motion. By using the method of transverse linearization for controller design, we achieve exponential orbital stability to a desired trajectory. Numerical simulations confirm this property and show good convergence to a desired periodic motion when initialized from a resting state.