Stabilization of an underactuated planar 2R manipulator

We describe a technique for the stabilization of a 2R robot moving in the horizontal plane with a single actuator at the base, an interesting example of underactuated mechanical system that is not smoothly stabilizable. The proposed method is based on a recently introduced iterative steering paradigm, which prescribes the repeated application of an error contracting open-loop control law. In order to compute efficiently such a law, the dynamic equations of the robot are transformed via partial feedback linearization and nilpotent approximation. Simulation and experimental results are presented for a laboratory prototype.