Robust orbital stabilization of pendubot: Algorithm synthesis, experimental verification, and application to swing up and balancing control

Motivated by applications where the natural operation mode is periodic, orbital stabilization of mechanical systems has received significant attention over the last few years (see, e.g., [24] and references therein). For these systems the orbital stabilization paradigm, referred to as periodic balancing [5], differs from typical formulations of output tracking where the reference trajectory to follow is known a priori. The control objective for the periodic balancing, e.g., a walking rabbit [6] is to result in the closed-loop system that generates its own periodic orbit similar to that produced by a nonlinear oscillator. Apart from this, the closed-loop system should be capable of moving from one orbit to another by simply modifying the orbit parameters such as frequency and/or amplitude.