Stable periodic motions of inertia wheel pendulum via virtual holonomic constraints

We present a new control strategy for an underactuated two-link robot, called inertia wheel pendulum. The system consists of a free planar rotational pendulum and a symmetric disk, attached to its end and directly controlled by a DC-motor. The goal is to create stable oscillations of the pendulum, which is not directly actuated. We exploit a recently proposed feedback control design strategy, based on motion planning via virtual holonomic constraints. This strategy is shown to be useful for design of regulators for achieving orbitally exponentially stable oscillatory motions. The main contribution is a step-by-step recipe on how to achieve oscillations with pre-specified amplitude from a given range and an arbitrary independently chosen period.