Second order averaging methods and oscillatory feedback control of underactuated mechanical systems

This paper considers the task of stabilizing underactuated mechanical systems via high-amplitude, high-frequency actuation. Using higher order averaging techniques, we extend previous work to the case where symmetric products of order higher than one are necessary for controllability. We first introduce a second order averaged mechanical system model that incorporates higher order terms. Using this result, we then construct controls that produce exponential stabilization or trajectory tracking through feedback of an error signal that is kept constant over whole periods of the oscillatory actuation. Simulations demonstrate the method.