  Collocated adaptive control of underactuated systems is still a main concern
for the control community, all the more so because the collocated dynamics is
no longer linear with respect to the constant base parameters. This work
extends and encompasses the well known adaptive control result for fully
actuated mechanical systems to the underactuated case. The key point is the
introduction of a fictitious control input that allows us to consider the
complete system dynamics, which is assumed to be linear with respect to the
base parameters. Local stability and convergence of time varying reference
trajectories for the collocated dynamics are demonstrated by using Lyapunov and
Barbalat arguments. Simulation and experimental results on a two-link
manipulator verify the soundness of the proposed approach.
