Almost-global tracking of the unactuated joint in a pendubot

Tracking the unactuated configuration variable in an underactuated system, in a global sense, has not received much attention. Here we present a scheme to do so for a pendubot a two link robot actuated only at the first link. We propose a control law that asymptotically tracks any smooth reference trajectory of the unactuated second joint , from almost-any initial condition, termed as almost-global asymptotic tracking (AGAT). Further, the actuated joint’s angular velocity remains bounded. We go on to generalize the proposed scheme to an n-link system with as many (or more) degrees of actuation than unactuation, and show that the result holds.