Control of an underactuated manipulator using similarities to the double integrator

A horizontally mounted two-link manipulator is considered. We assume that only the first joint is actuated, while the second joint is passive and frictionless. The system exposes challenging properties, e. g. it is not controllable in the equilibrium points. We transform the equations of motion in Byrnes-Isidori normal form and consider the projection into the subspace spanned by the velocity-like state variables. From this viewpoint the manipulator system reveals qualitative similarities to the well-understood double integrator. In particular the drift vector field is investigated. Exploiting these similarities, an approach for equilibrium point transition based on sliding mode control is proposed.