Controllability of under-actuated planar manipulators with one unactuated joint

This paper is concerned with the analysis of controllability for a class of nonholonomic systems. We discuss the controllability of under-actuated planar manipulators with one unactuated joint. We show that these systems are completely controllable if the first joint (in the base side) is actuated. In order to prove this, we use a kind of bi-directional approach.