  In this paper, the notion of contraction is used to solve the
trajectory-tracking problem for a class of mechanical systems. Additionally, we
propose a dynamic extension to remove velocity measurements from the controller
while rejecting matched disturbances. In particular, we propose three control
designs stemming from the Interconnection and Damping Assignment
Passivity-Based Control approach. The first controller is a tracker that does
not require velocity measurements. The second control design solves the
trajectory-tracking problem while guaranteeing robustness with respect to
matched disturbances. Then, the third approach is a combination of both
mentioned controllers. It is shown that all proposed design methods guarantee
exponential convergence of the mechanical system to the desired (feasible)
trajectory due to the contraction property of the closed-loop system. The
applicability of this method is illustrated via the design of a controller for
an underactuated mechanical system.
