Almost-global tracking of the unactuated joint in a pendubot

TL;DR

This paper introduces a control scheme for almost-global asymptotic tracking of the unactuated joint in a pendubot, extending the approach to systems with multiple links and degrees of actuation.

Contribution

It presents a novel control law enabling almost-global tracking of the unactuated joint in a pendubot and generalizes this method to multi-link systems with various actuation configurations.

Findings

Achieves almost-global asymptotic tracking for the unactuated joint.

Extends the control scheme to n-link systems with multiple degrees of actuation.

Demonstrates the effectiveness of the control law through theoretical analysis.

Abstract

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 for almost-global asymptotic tracking (AGAT) of a smooth reference trajectory for the unactuated second joint of the pendubot. The control law achieves almost-global tracking for any smooth reference trajectory specified for the unactuated joint. Further, we 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.