Stabilization of underactuated robots: theory and experiments for a planar 2R manipulator

We outline a general approach for the stabilization of robots with passive joints, an interesting example of mechanical systems that may not be controllable in the first approximation. The proposed method is based on a recently introduced iterative steering paradigm, which prescribes the repeated application of a contracting open-loop control law. In order to complete efficiently such a law, the dynamic equations of the robot are put in a suitable form, via partial feedback linearization and approximate nilpotentization. The design procedure is illustrated for a 2R robot moving in the horizontal plane with a single actuator at the base. Experimental results are presented for a laboratory prototype