Feedback linearization of the transverse dynamics for a class of one degree underactuated systems

This paper investigates feedback linearization of one degree underactuated systems the mass matrix of which does not depend on the unactuated variable. We study the dynamics of such systems in a new time scale τ. In this new time scale, we exhibit a set of coordinates for which the dynamics transverse to a particular one-dimensional manifold is dynamic feedback linearizable. To this end, we design a relative degree three output with respect to one input and use dynamic extension. We then introduce a new motion planning algorithm for this class of systems.